Name: ________________________ Class: ___________________ Date: __________
ID: Practice
Geom_Fin_Exam_Practice
Multiple Choice
Identify the choice that best completes the statement or answers the question.
G:1.01 Use the trignonometric ratios to model and solve problems involving right triangles.
4. KM is an altitude of JKL, and KM ≅ JM . The
measure of ∠LKM is 55 0 , and ML = 12 cm.
1. Billy is 74 in. tall, and his shadow is 70 in.
long. What is the approximate angle of
elevation of the sun?
a.
b.
c.
d.
19 0
43 0
47 0
71 0
What is the approximate length of JK ?
a.
b.
c.
d.
2. A truck is at the top of a ramp as shown below.
8.4 cm
11.9 cm
20.7 cm
24.2 cm
5. The angle of elevation from point G on the
ground to the top of a flagpole is 20. The
height of the flagpole is 60 feet.
Approximately how high above the ground is
the truck?
a. 4.45 m
b. 3.59 m
c. 1.95 m
d. 1.75 m
Which equation could find the distance from
point G to the base of the flagpole?
a.
3. A right triangle is shown below.
b.
c.
d.
What is the approximate value of h?
a.
b.
c.
d.
x
60
60
sin 20 0 =
x
60
tan 20 0 =
x
x
tan 20 0 =
60
sin 20 0 =
6. A mountain climber stands on level ground 300
100 meters
115 meters
140 meters
173 meters
m from the base of a cliff. The angle of
elevation to the top of the cliff is 58 0 . What is
the approximate height of the cliff?
a.
b.
c.
d.
25
566 m
480 m
354 m
187 m
Name: ________________________
ID: Practice
7. A 20-foot ladder is leaning against a wall. The
9. Susan is making a small cone out of paper. The
foot of the ladder is 7 feet from the base of the
wall. What is the approximate measure of the
angle the ladder forms with the ground?
a.
b.
c.
d.
cone has a radius of 13.2 cm, and the angle
between the lateral surface and the base is
38.6 0 . The formula for the lateral area, s, of a
cone is s = π rl, where r is the radius and l is the
70.7 0
69.5 0
20.5 0
19.3 0
slant height. What is the cone’s approximate
lateral area?
a. 340 cm2
b. 430 cm2
c. 700 cm2
d. 800 cm2
8. A ladder is leaning against the side of a
building. The ladder is 30 feet long, and the
angle between the ladder and the building is
15 0 . About how far is the foot of the ladder
from the
building?
a.
b.
c.
d.
10. A dead tree was struck by lightning, causing it
to fall over at a point 10 ft up from its base.
7.76 feet
8.04 feet
18.37 feet
28.98 feet
If the fallen treetop forms a 40 0 angle with the
ground, about how tall was the tree originally?
a.
b.
c.
d.
13 ft.
16 ft.
23 ft.
26 ft.
G:1.02 Use length, area, and volume of geometric figures to solve problems. Include arc length,
area of sectors of circles; lateral area, surface area, and volume of three-dimensional
figures; and perimeter, area, and volume of composite figures.
11. What is the approximate area of a 70 0 sector of
13. The midpoint of PQ is R. R has coordinates
ÊÁ −3,2,−1 ˆ˜ and P has coordinates ÊÁ 4,−6,−6 ˆ˜ .
Ë
¯
Ë
¯
a circle with a radius of 8 inches?
a.
b.
c.
d.
5 in. 2
10 in. 2
39 in. 2
156 in. 2
What are the coordinates of Q?
a.
b.
c.
12. JK and LM are perpendicular diameters of a
circle. They are each 12 inches long. What is
the approximate length of chord LK ?
a.
b.
c.
d.
d.
17 in.
12 in.
10.4 in.
8.5 in.
2
ÊÁ −10,10,4ˆ˜
Ë
¯
ÊÁ −3.5,4,2.5 ˆ˜
Ë
¯
ÊÁ 0.5,−2,−3.5 ˆ˜
Ë
¯
ÊÁ 11,−14,−11ˆ˜
Ë
¯
Name: ________________________
ID: Practice
14. A cone has a radius of 12 cm and a height of 9
18. A container in the shape of a rectangular prism
cm. What is the approximate lateral surface
area of the cone? (To calculate the lateral
surface area, A, use the formula A = π rl, where
r is the radius and l is the slant height.)
has a base that measures 20 centimeters by 30
centimeters and has a height of 15 centimeters.
The container is partially filled with water. A
student adds more water to the container and
notes that the water level rises 2.5 cm. What is
the volume of the added water?
a.
b.
c.
d.
89 cm2
123 cm2
424 cm2
565 cm2
a.
b.
c.
d.
15. A garden has the shape of an isosceles right
triangle. The length of the hypotenuse is 24
feet. What is the area of the garden?
a.
b.
c.
d.
1,500 cm3
3,600 cm3
4,500 cm3
9,000 cm3
19. Katie, a gardener, needs to put grass seeds on
2
576 ft
288 ft 2
203 ft 2
144 ft 2
the triangle formed by the 3 roads below. Each
side of the grass triangle is 350 ft long.
16. The perimeter of a regular hexagon is 48 ft.
What is the approximate area of this polygon?
a.
b.
c.
d.
288 ft 2
166 ft 2
96 ft 2
28 ft 2
If one bag of seed covers 10,000 ft 2 , how many
bags will Katie need to buy?
17. A plastic tray is shown below, with the
dimensions labeled. The tray does not have a
cover on top. The bottom and two of the sides
are rectangles. The remaining two sides are
congruent isosceles trapezoids.
a.
b.
c.
d.
5
6
7
8
20. What is the approximate surface area of a right
hexagonal prism with a base perimeter of 96
meters and a height of 10 meters? (Use
S = ap + ph , where a is the apothem of the base,
p is the perimeter of the base, and h is the
height of the prism.)
a.
b.
c.
d.
What is the total area of the outer surface of the
tray?
a.
b.
c.
d.
495 cm2
584 cm2
615 cm2
975 cm2
3
3,620 m2
2,290 m2
1,728 m2
1,625 m2
Name: ________________________
ID: Practice
21. The ratio of the height of the pyramid to the
24. A sign is shaped like an equilateral triangle.
edge of the square base is 1.5 to 1. The height
of the pyramid is 3 meters. What is the
approximate length of the slant height of the
pyramid?
a.
b.
c.
d.
4.4 m
3.2 m
2.8 m
1.4 m
If one side of the sign is 36 inches, what is the
approximate area of the sign?
22. A rectangular prism is 40 ft by 38 ft by 15 ft.
Shown below is the prism with a half
cylinder removed.
a.
b.
c.
d.
1,296 in. 2
648 in. 2
561 in. 2
108 in. 2
25. An inflated round balloon with radius r = 50
centimeters holds approximately 523,600 cubic
centimeters of air. When the balloon is
contracted such that the radius is
2
the original
3
size, what is the approximate volume of the
partially deflated balloon?
Approximately what volume of the original
prism remains?
a. 22,800 cubic feet
b. 19,792 cubic feet
c. 19,560 cubic feet
d. 17,651 cubic feet
23. An apple pie is cut into six equal slices as
shown below.
a.
b.
c.
d.
1.94 × 10 4 cm3
1.55 × 10 5 cm3
1.75 × 10 5 cm3
3.49 × 10 5 cm3
26. What is the approximate area of the trapezoid?
a.
b.
c.
d.
If the diameter of the pie is ten inches, what is
the approximate arc length of one slice of pie?
a. 1.67 in.
b. 3.14 in.
c. 5.24 in.
d. 13.08 in.
83 cm2
110 cm2
128 cm2
192 cm2
27. What is the approximate distance between the
points ÊÁË 750, 900, 1,500 ˆ˜¯ and ÊÁË 950, 800, 550ˆ˜¯ ?
a.
b.
c.
d.
4
976 units
1,025 units
2,062 units
952,500 units
Name: ________________________
ID: Practice
28. What is the ratio of the surface areas of two
spheres with volumes of 64 cm3 and 125 cm3 ?
a. 4 : 5
b. 8 : 10
c. 16 : 25
d. 64 : 125
G:1.03 Use length, area, and volume to model and solve problems involving probability.
31. A number line is shown below.
29. A rectangle contains two inscribed semicircles
and a full circle, as shown below.
Point P will be picked at random on EK . What is
the probability that P will be on FK ?
4
a.
6
3
b.
4
4
c.
5
5
d.
6
If a point is chosen at random inside the
rectangle, what is the approximate probability
that the point will also be inside the shaded
region?
a.
b.
c.
d.
85%
79%
75%
50%
30. In order to win a game, Sheila must spin a 7 on
the spinner below.
If the spinner is fair, what is the probability
that she will spin a 7?
a.
b.
c.
d.
1
12
1
6
3
10
5
12
5
Name: ________________________
ID: Practice
32. A cylinder with a height of 6 inches and a
34. A circle is inscribed in a square, as shown
radius of 3 inches is inside a rectangular prism,
as shown below.
below.
If a point is randomly chosen inside the square,
what is the approximate chance that the point
lies outside the circle?
a. 21%
b. 27%
c. 73%
d. 79%
35. A cube is painted as shown. The three faces
that are not seen are not painted.
A point inside the rectangular prism will be
chosen randomly. What is the probability
that the point will also be inside the cylinder?
a. 5.2%
b. 7.9%
c. 15.7%
d. 23.6%
33. A point is randomly selected on XY . What is
the probability that it will be closer to the
midpoint of XY than to either X or Y ?
a.
b.
c.
d.
If a point on the surface of the cube is
randomly chosen, what is the probability that it
will lie in the painted area?
a.
b.
1
4
1
3
1
2
3
4
c.
d.
6
1
4
1
3
3
8
1
2
Name: ________________________
ID: Practice
36. A cube with edges 10 cm long is painted red. It
37. To win a carnival game, Keisha must throw a
is cut into smaller cubes with edges 2 cm long
that are placed into a bag. One small cube is
pulled out of the bag without looking. What is
the probability of pulling out a cube with three
of its faces painted red?
a.
b.
c.
d.
dart and hit one of 25 circles in a dart board
that is 4 feet by 3 feet. The diameter of each
circle is 4 inches.
4
125
8
125
2
25
12
125
Approximately what is the probability that a
randomly thrown dart that hits the board would
also hit a circle?
a. 18%
b. 26%
c. 63%
d. 73%
G:2.01 Use logic and deductive reasoning to draw conclusions and solve problems.
38. Which statement is logically equivalent to the
39. What is the inverse of the statement in the box?
given statement?
If a polygon is regular, then
it is convex.
If a quadrilateral is a
rhombus, then it is a
parallelogram.
a.
b.
c.
d.
If a polygon is not regular, then it
is not convex.
b. If a polygon is convex, then it is
regular.
c. If a polygon is not regular, then it
is convex.
d. If a polygon is not convex, then it
is not regular.
40. What is the converse of the statement in the
box?
a.
If a quadrilateral is a parallelogram, then it
is a rhombus.
If a quadrilateral is not a rhombus, then it is
not a parallelogram.
If a quadrilateral is not a rhombus, then it is
a parallelogram.
If a quadrilateral is not a parallelogram,
then it is not a rhombus.
If today is Saturday, then there
is no school today..
a.
b.
c.
d.
7
If there is no school today, then today is
Saturday.
If there is school today, then today is not
Saturday.
If today is not Saturday, then there is
school today.
If today is not Saturday, then there is no
school today.
Name: ________________________
ID: Practice
41. The conditional statement “all 45 0 angles are acute
angles” is true. Based on this conditional
statement, which of the following can be concluded
from the additional statement “the measure of ∠A is
45 0 ”?
a. The complement of ∠A is not an acute angle.
b. The supplement of ∠A is an acute angle.
c. ∠A is an acute angle.
d. ∠A is not an acute angle.
42.
MNO is shown below.
44. Which statement is the inverse of the statement
in the box?
If a quadrilateral is a
rectangle, then it is a
parallelogram.
If a quadrilateral is not a parallelogram,
then it is not a rectangle.
b. If a quadrilateral is a parallelogram, then it
is a rectangle.
c. If a quadrilateral is not a rectangle, then it
is not a parallelogram.
d. A quadrilateral is a rectangle if and only if
it is a parallelogram.
45. Given:
If there was lightning, then we did not
swim.
If there was lightning, then we did not jog.
Using either one or both of the given
statements, which conclusion is valid?
a. If we did not swim, then we did not jog.
b. If we did not jog, then there was lightning.
c. If we did swim, then we did not jog.
d. If we did jog, then there was not lightning.
46. Given the statements:
a.
Which statement about this triangle is true?
a. m∠O > m∠M
b. m∠M > m∠N
c. m∠M < m∠N
d. m∠N < m∠O
43. What is the contrapositive of the statement
below?
If a triangle is isosceles,
then it has two congruent
sides.
a.
b.
c.
d.
Linear pairs are supplementary.
If a triangle does not have two congruent
sides, then it is not isosceles.
If a triangle is isosceles, then it does not
have two congruent sides.
If a triangle has two congruent sides, then it
is isosceles.
If a triangle is not isosceles, then it does not
have two congruent
sides.
∠1 and ∠2 are supplementary.
Using either one or both of the given
statements, which conclusion is valid?
a.
b.
c.
d.
8
∠1 and ∠2 form a linear pair.
Angles that are not supplemtary are not linear
pairs.
∠1 ≅ ∠2
Supplementary angles are linear pairs.
Name: ________________________
ID: Practice
G:2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and
write proofs.
47. In the diagram below, j⊥m and k⊥m.
50. The slope of a line tangent to a circle is
2
.
5
What is the slope of the line that passes
through the point of tangency and the center of
the circle?
a.
b.
c.
What is m∠1?
a. 39
b. 47
c. 51
d. 129
d.
5
2
2
−
5
2
5
5
2
−
⎯⎯
→
⎯⎯
⎯
→
51. In the figure below, SR | | UV .
⎯⎯
⎯
→
48. In the figure below, WY bisects ∠VWZ,
m∠VWY = 32, and m∠VWX = 117.
What is m∠STU?
a. 60 0
b. 90 0
c. 1200
d. 2400
⎯⎯
⎯
→
⎯⎯
⎯
→
52. OX is the bisector of ∠WOZ, and OY is the
bisector of ∠XOZ.
What is m∠ZWX ?
a. 85
b. 53
c. 42.5
d. 26.5
49. M is the midpoint of RS , RM = (3x + 1) , and
MS = (4x − 2) . What is RS ?
a. 20
b. 17
c. 10
d. 3
If m∠YOZ = 26.5, what is m∠WOZ?
a. 53.0 0
b. 79.5 0
c. 106.0 0
d. 132.5 0
9
Name: ________________________
ID: Practice
⎯⎯
⎯
→
53. Given ∠VYX is bisected by YW ,
m∠VYX = (6r − 18) , and m∠VYW = 36. What is
the value of r?
a. 15
b. 30
c. 36
d. 72
54. According to the map, the road connecting the
56. In the diagram below, MN⊥JL.
cities of Oakton (O) and Ridgeton (R)
intersects the road connecting Maple View (M)
and Pineville (P).
Which statement must be true?
a. m∠PKN = m∠JKP
b. m∠PKN = 90 0 + m∠JKP
c. m∠PKN = 180 0 − m∠JKP
d. m∠PKN = 270 0 − m∠JKP
57. Given: k Ä m Ä n
If the roads intersect in the town of Forest
Grove (F) in the diagram, which statement is
always true?
a.
b.
c.
d.
MP = RO
PF⊥OF
∠OFP ≅ ∠RFM
∠RFP ≅ ∠MFR
Which statement justifies the conclusion that
∠1 ≅ ∠2 ≅ ∠3?
a. If k Ä m Ä n and are cut by transversal t, then
alternate interior angles are congruent.
b. If k Ä m Ä n and are cut by transversal t, then
vertical angles are congruent.
c. If k Ä m Ä n and are cut by transversal t, then
alternate exterior angles are congruent.
d. If k Ä m Ä n and are cut by transversal t, then
corresponding angles are congruent.
55. Given LP, LM = (3x + 1) , MN = (4x − 3) ,
NP = (6x − 5) , and LM ≅ NP.
What is the length of MP?
a. 2
b. 7
c. 12
d. 19
10
Name: ________________________
ID: Practice
60. ∠XYZ shown below has a measure of (8x + 12) .
0
58. In the diagram, GH Ä IJ.
The measure of ∠1 is (4x + 8) , and the measure of
0
∠2 is (9x − 11) .
0
If m∠GLK = 55 0 and m∠EFJ = 120 0 , which is
m∠KEF ?
a. 55 0
b. 60 0
c. 65 0
d. 70 0
←⎯
⎯
→
What is the measure of ∠XYZ?
a. 3 0
b. 20 0
c. 36 0
d. 60 0
61. In the drawing, what is the measure of angle y?
←⎯⎯
→
59. Given RS Ä TU , m∠7 = (3x − 10) , and
m∠3 = (2x + 5) .
a.
b.
c.
d.
What is m∠1?
a. 1450
b. 75 0
c. 35 0
d. 15 0
11
40 0
60 0
80 0
1000
Name: ________________________
ID: Practice
1
3
x + 4, m∠SQT = x − 6, and
2
4
m∠RQT = 2x − 47.
62. Given m∠RQS =
What is m∠RQS ?
a.
b.
c.
d.
24 0
34 0
39 0
60 0
12
Name: ________________________
ID: Practice
G:2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems
and write proofs: a) Triangles b) Quadrilaterals c) Other Polygons d) Circles
63. Given: ABCD is an isosceles trapezoid. M is the midpoint of AB.
Prove: DM ≅ CM
What is the missing statement and reason that completes the proof shown above?
a.
b.
64.
AD ≅ BC ; the legs of an isosceles
trapezoid are congruent.
∠MAD ≅ ∠MBC ; the base angles of an
isosceles trapezoid are congruent.
c.
d.
AM ≅ BM ; the corresponding parts of
congruent triangles are congruent.
∠ABC ≅ ∠DAB; if lines are parallel,
interior angles on the same side of a
transversal are supplementary..
WXYZ is a parallelogram. If m∠W = 40, what is
m∠Z?
a. 40
b. 50
c. 140
d. 150
66. In the diagram below, PQ ≅ MQ and m∠M = 70.
65. What is the measure of an interior angle of a
What is m∠TQP?
a. 70
b. 110
c. 140
d. 150
regular polygon with 16 sides?
a.
b.
c.
d.
0
22.5
25.7 0
157.5 0
205.7 0
13
Name: ________________________
ID: Practice
67. Given parallelogram EFGH , what is the length of
side EF ?
a.
b.
c.
d.
27
21
19
7
68. Circles P, Q, and R are shown below. The diameter of circle R is 22.
What is the length of PR?
a. 25
b. 34
c.
d.
39
50
69. Based on the coordinates E ÁÊË −2,−3 ˜ˆ¯ , F ÁÊË 3,−3 ˜ˆ¯ ,
G ÊÁË 6,1 ˆ˜¯ , H ÊÁË 3,5 ˆ˜¯ , I ÊÁË −2,5 ˆ˜¯ , and J ÊÁË 1,1 ˆ˜¯ , what best
describes polygon EFGHIJ?
a. equilateral convex
b. equilateral concave
c. equiangular concave
d. equiangular convex
70. Which parts must be congruent to prove
PQR ≅ PSR by SAS?
14
a.
∠Q ≅ ∠S and QP ≅ SP
b.
∠Q ≅ ∠S and QR ≅ SR
c.
∠QRP ≅ ∠SRP and QP ≅ SP
d.
∠QPR ≅ ∠SPR and QP ≅ SP
Name: ________________________
ID: Practice
75. A regular octagon is inscribed in a circle. What
71. How long is EF ?
is the degree measure of each arc joining the
consecutive vertices?
a.
b.
c.
d.
a. 40 0
b. 45 0
c. 54 0
d. 60 0
76. If KLMN is a rhombus, and m∠KLM = 80, what is
the measure of ∠1?
20 ft
25 ft
30 ft
35 ft
72. In circle O shown below, RS ≅ ST .
a.
b.
c.
d.
What kind of triangle is RST ?
a. right
b. acute
c. obtuse
d. scalene
73. Figure JKLM is a parallelogram.
40 0
50 0
80 0
90 0
77. The measure of each exterior angle of a regular
polygon is 45 0 . How many sides does the
polygon have?
a.
b.
c.
d.
4
5
8
9
78. In a hexagon, three angles have the same
measure. The measure of each of the congruent
angles is twice the measure of the fourth angle
and is half the measure of the fifth angle. The
sixth angle measures 1150 . What is the measure
of the smallest angle?
What is the value of x?
a. 65 0
b. 55 0
c. 45 0
d. 35 0
a.
b.
c.
d.
74. What is the measure of an interior angle of a
regular hexagon?
a.
b.
c.
d.
45 0
60 0
1200
1350
15
41 0
55 0
1100
1210
Name: ________________________
ID: Practice
79. In the circle below, what is the value of x?
82. A gardener wants to enclose a circular garden
with a square fence, as shown below.
If the circumference of the circular garden is
about 48 feet, which of the following is the
approximate length of fencing needed?
a.
b.
c.
d.
a.
b.
c.
d.
4 units
6 units
7 units
9 units
31 ft.
61 ft.
122 ft.
244 ft.
83. The vertices of a hexagon are ÊÁË 6,7 ˆ˜¯ , ÊÁË 9,1 ˆ˜¯ ,
ÊÁ 6,−4ˆ˜ , ÊÁ −1,−4 ˆ˜ , ÊÁ −6,1 ˆ˜ , and ÊÁ −1,7 ˆ˜ . Which best
Ë
¯ Ë
¯ Ë
¯
Ë
¯
describes the hexagon?
a. nonregular and convex
b. nonregular and concave
c. regular and convex
d. regular and concave
84. Jill wants to measure the width of a river. She
80. In JKLM , JK⊥KL and JK Ä ML.
What is the area of the trapezoid?
a. 120 sq cm
b. 144 sq cm
c. 164 sq cm
d. 168 sq cm
81. A triangle has side lengths of 10 cm, 15 cm,
and 20 cm. Which side lengths form the largest
angle?
a. 5 cm, 10 cm
b. 10 cm, 15 cm
c. 10 cm, 20 cm
d. 15 cm, 20 cm
marks distances as shown in the diagram.
Using this information, what is the
approximate width of the river?
a. 6.6 yards
b. 10 yards
c. 12.8 yards
d. 15 yards
85. The exterior angle of a base angle in an
isosceles triangle is 1000 . What is the measure
of
the vertex angle?
a.
b.
c.
d.
16
20 0
40 0
60 0
80 0
Name: ________________________
ID: Practice
SRU is shown below.
87. If PQRS is a rhombus, which statement must be
true?
86. Right
What is the length of RS ?
a.
84
a.
b.
c.
74
60
35
b.
c.
d.
d.
∠PSR is a right angle.
PR ≅ QS
∠PQR ≅ ∠QRS
PQ ≅ QR
G:2.04 Develop and apply properties of solids to solve problems.
90. Kevin’s teacher gave him the following pieces of
cardboard.
88. Which pattern would fold to make a pyramid
with a square base?
2
equilateral
triangles:
a.
4 squares:
b.
Which polyhedron can Kevin build using some or
all of these pieces?
a. a triangular prism
b. a rectangular prism
c. a triangular pyramid
d. a square pyramid
c.
91. A plane intersects a sphere that has a radius of
13 cm. The distance from the center of the
sphere to the closest point on the plane is 5 cm.
What is the radius of the circle that is the
intersection of the sphere and the plane?
d.
89. A regular tetrahedron is a triangular pyramid.
What is the total surface area of a regular
tetrahedron with base edges of 7 cm?
a.
b.
c.
d.
7
14
28
49
a.
b.
c.
d.
3 cm2
3 cm2
3 cm2
3 cm2
17
8 cm
10 cm
12 cm
13 cm
Name: ________________________
ID: Practice
94. In the picture below, what are the coordinates
92. What is the best description of the solid figure
of P?
shown below?
a.
b.
c.
d.
a regular polygon
a convex polygon
a regular polyhedron
a nonregular polyhedron
93. What are the coordinates of vertex K for the
cube shown below?
a.
b.
c.
d.
ÊÁ 0,6,6 ˆ˜
Ë
¯
ÊÁ −6,0,6 ˆ˜
Ë
¯
ÁÊ −6,6,0 ˜ˆ
Ë
¯
ÁÊ 6,−6,6 ˜ˆ
Ë
¯
95. A spherical foam ball, 10 inches in diameter, is
used to make a tabletop decoration for a
party. To make the decoration sit flat on the
table, a horizontal slice is removed from the
bottom of the ball, as shown below.
a.
b.
c.
d.
ÊÁ −3,3,0 ˆ˜
Ë
¯
ÊÁ −3,0,3 ˆ˜
Ë
¯
ÊÁ 0,3,−3 ˆ˜
Ë
¯
ÊÁ 3,−3,0 ˆ˜
Ë
¯
If the radius of the flat surface formed by the
cut is 4 inches, what is the height of the
decoration?
a. 10 in.
b. 8 in.
c. 6 in.
d. 4 in.
18
Name: ________________________
ID: Practice
96. What is the approximate surface area of a
98. The intersection of a sphere and a plane is a
regular tetrahedron with edge length 12 cm?
166.3 sq cm
187.1 sq cm
249.4 sq cm
498.8 sq cm
97. Two tetrahedra are congruent. One tetrahedron
is glued to the other so that the glued faces of
the two tetrahedra completely cover each other,
producing a new polyhedron. How many faces
does the new polyhedron have?
circle with a radius of 8 cm. If the sphere has a
radius of 18 cm, how far is the plane from the
center of the sphere?
a. 16.12 cm
b. 14.97 cm
c. 10.00 cm
d. 8.00 cm
99. A regular octahedron has eight faces that are
congruent equilateral triangles. How many
edges does a regular octahedron have?
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
6
7
8
9
12
16
17
24
G:3.01 Describe the transformation (translation, reflection, rotation, dilation) of polygons in the
coordinate plane in simple algebraic terms.
100. A translation is applied to
FGH , forming
F ′G ′H ′. If the translation is described by ÊÁË x ′, y ′ ˆ˜¯ = ÊÁË x + 2, y − 3 ˆ˜¯ ,
which graph shows the translation correctly?
a.
c.
b.
d.
19
Name: ________________________
ID: Practice
GHI will be dilated by a scale factor of 3,
resulting in G ′H ′I ′. What rule describes this
transformation?
ÊÁ 1 1 ˆ˜
a. ÊÁË x ′,y ′ ˆ˜¯ = ÁÁÁÁ x, y ˜˜˜˜
Ë3 3 ¯
b. ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË 3x,3y ˆ˜¯
c. ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË x + 3,y + 3 ˆ˜¯
d. ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË x − 3,y − 3 ˆ˜¯
102.
PQR, shown below, will be rotated clockwise
101.
103.
SLM is rotated 1800 about the origin, what
will be the coordinates for the image of M ?
If
1800 about the origin.
a.
b.
c.
Which rule describes the transformation?
a. ÁÊË x ′,y ′ ˜ˆ¯ = ÁÊË x,y ˜ˆ¯
b. ÁÊË x ′,y ′ ˜ˆ¯ = ÁÊË −x,y ˜ˆ¯
c. ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË x,−y ˆ˜¯
d. ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË −x,−y ˆ˜¯
d.
ÊÁ 5,5ˆ˜
Ë ¯
ÊÁ 5,−5ˆ˜
Ë
¯
ÊÁ −5,5ˆ˜
Ë
¯
ÊÁ −5,−5 ˆ˜
Ë
¯
104. What is the rule for the transformation formed
by a translation 2 units to the left and 3 units up
followed by a 90 0 counterclockwise rotation?
a.
b.
c.
d.
20
ÊÁ x ″,y ″ ˆ˜ = ÊÁ −3x,−2y ˆ˜
Ë
¯ Ë
¯
ÊÁ x ″,y ″ ˆ˜ = ÊÁ x − 2,y + 3 ˆ˜
¯
Ë
¯ Ë
ÊÁ x ″,y ″ ˜ˆ = ÊÁÁ − ÊÁ y + 3ˆ˜ ,x − 2 ˆ˜˜
¯
Ë
¯ Ë Ë
¯
ÊÁ x ″,y ″ ˜ˆ = ÁÊÁ − ÊÁ y − 2ˆ˜ ,x + 3 ˜ˆ˜
¯
Ë
¯ Ë Ë
¯
Name: ________________________
105.
G ′H ′I ′ is the image of
transformation.
ID: Practice
107. Triangle PQR has vertices P ÁÊË −1,3 ˜ˆ¯ , Q ÁÊË 1,2 ˜ˆ¯ , and
R ÊÁË −2,−1ˆ˜¯ . When PQR is reflected over the line
y = −2, what are the coordinates of P ′?
a. ÊÁË −1,−3 ˆ˜¯
b. ÊÁË −1,−7 ˆ˜¯
c. ÁÊË −2,−2 ˜ˆ¯
d. ÁÊË −3,−3 ˜ˆ¯
108.
P ′Q ′R ′ is the image produced aftet reflecting
PQR across the y − axis. If P has coordinates
ÊÁ s,t ˆ˜ , what are the coordinates of P ′?
Ë ¯
a. ÊÁË t,s ˆ˜¯
b. ÊÁË s,−t ˆ˜¯
c. ÁÊË −s,−t ˜ˆ¯
d. ÁÊË −s,t ˜ˆ¯
GHI after a
Which choice describes the transformation
shown?
reflection over the x − axis
reflection over the y − axis
ÊÁ x ′,y ′ ˆ˜ = ÊÁ x − 8,y ˆ˜
Ë
¯ Ë
¯
d. ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË x,y − 8 ˆ˜¯
106. In the diagram below, P ′Q ′R ′ is the image
produced by applying a transformation to PQR.
a.
b.
c.
109. Point J ÊÁË p,q ˆ˜¯ is a vertex of quadrilateral JKLM .
What are the coordinates of J ′ after JKLM is
rotated 1800 about the origin?
a. ÊÁË −p,−q ˆ˜¯
b. ÊÁË −p,q ˆ˜¯
c. ÊÁË p,−q ˆ˜¯
d. ÁÊË q,−p ˜ˆ¯
110. The point G ÊÁË 2,−7 ˆ˜¯ is transformed according to the
rule ÊÁË x ′,y ′ ˆ˜¯ = ÊÁË x + 2,y − 3 ˆ˜¯ . The image G ′ of the
transformation is then reflected over the line y = x,
resulting in point G ′. What are the coordinates of
G ″?
a. ÊÁË 4,10 ˆ˜¯
b. ÁÊË 4,−10 ˜ˆ¯
c. ÁÊË −10,4 ˜ˆ¯
d. ÊÁË −4,10 ˆ˜¯
Which rule describes the transformation?
a. (x' , y' ) = (x, y)
b. (x' , y' ) = (−x, −y)
c. (x' , y' ) = (−x, y)
d. (x' , y' ) = (x, −y)
21
Name: ________________________
ID: Practice
112. Point P ′ is the image of point P after a
counterclockwise rotation of 90 0 about the origin.
If the coordinates of P ′ are ÁÊË −7,3 ˜ˆ¯ , what are the
111. Point J ÁÊË p,q ˜ˆ¯ is a vertex of JKL. What are the
coordinates of J ′ after JKL is reflected across the
line y = x?
a. ÊÁË −p,−q ˆ˜¯
b. ÊÁË p,−q ˆ˜¯
c. ÊÁË q,−p ˆ˜¯
d. ÊÁË q,p ˆ˜¯
coordinates of point P?
a. ÁÊË −3,−7 ˜ˆ¯
b. ÁÊË −3,7 ˜ˆ¯
c. ÊÁË 3,−7 ˆ˜¯
d. ÊÁË 3,7 ˆ˜¯
113.
of the area of
X ′Y ′Z ′ ?
a. 4 :1
b. 2 :1
c. 1 :2
d. 1 :4
22
1
. What is the ratio
2
XYZ to the area of its image,
XYZ is dilated by a factor of
Name: ________________________
G3.02
114.
ID: Practice
Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to
describe the transformation of polygons in the coordinate plane.
ÈÍ
˘˙
ÍÍ
˙
ÍÍ −2 2
3 ˙˙˙˙
The vertex matrix for PQR is ÍÍÍ
˙˙ .
ÍÍ
˙
ÍÎ −2 4 −3 ˙˙˚
The graph below shows PQR and its image,
P ′Q ′R ′ , after a transformation.
115. The vertex matrtix for
a.
b.
c.
d.
2
5
˘˙
˙
4 ˙˙˙˙
˙˙ .
˙
3 ˙˙˚
JKL is translated 2 units right and
3 units up, resulting in J ′K ′L ′. A translation
of 4 units left and 1 unit up is applied to
J ′K ′L ′ , resulting in J ″K ″L ″. Which matrix
expression gives the vertex matrix for
J ″K ″L ″?
ÈÍ
ÍÍ
Í −2 2
a. ÍÍÍÍ
ÍÍ
ÍÎ 1 5
ÈÍ
ÍÍ
Í −2 2
b. ÍÍÍÍ
ÍÍ
ÍÎ 1 5
ÈÍ
ÍÍ
Í −2 2
c. ÍÍÍÍ
ÍÍ
ÍÎ 1 5
ÈÍ
ÍÍ
Í −2 2
d. ÍÍÍÍ
ÍÍ
ÍÎ 1 5
˘˙ ÈÍ
˙ Í
4 ˙˙˙˙ ÍÍÍÍ 2
˙˙ + ÍÍ
˙ Í
3 ˙˙˚ ÍÍÎ 3
˘˙ ÈÍ
˙ Í
4 ˙˙˙˙ ÍÍÍÍ −4
˙˙ + ÍÍ
˙ Í
3 ˙˙˚ ÍÍÎ 1
˘˙ ÈÍ
˙ Í
4 ˙˙˙˙ ÍÍÍÍ 2
˙˙ + ÍÍ
˙ Í
3 ˙˙˚ ÍÍÎ 2
˘˙ ÈÍ
˙ Í
4 ˙˙˙˙ ÍÍÍÍ −2
˙˙ + ÍÍ
˙ Í
3 ˙˙˚ ÍÍÎ 4
˘˙
˙
2 ˙˙˙˙
˙˙
˙
3 ˙˙˚
2
3
−4
1
2
2
−2
4
˘˙
˙
2 ˙˙˙˙
˙˙
˙
2 ˙˙˚
˘˙
˙
−4 ˙˙˙˙
˙˙
˙
1 ˙˙˚
˘˙
˙
−2 ˙˙˙˙
˙˙
˙
4 ˙˙˚
ÈÍ
˘˙
ÍÍ
˙˙
ÍÍ −2
˙˙
3
2
Í
˙˙ .
116. The vertex matrix for RST is ÍÍ
˙˙
ÍÍ
ÍÎ −3 −1 −4 ˙˙˚
R ′S ′T ′ is the image produced by translating
RST 3 units left and 4 units up. What is the
vertex matrix for R ′S ′T ′?
˙˘˙
ÍÈÍ
˙˙
ÍÍ −5
0
−1
˙˙
Í
a. ÍÍÍ
˙˙
˙
ÍÍ
ÍÎ −7 −5 −8 ˙˙˚
˙˘
ÍÈÍ
ÍÍ −5 0 −1 ˙˙˙
˙˙
Í
b. ÍÍÍ
˙˙
˙
ÍÍ
ÍÎ 1 3
0 ˙˙˚
ÈÍ
˘˙
˙˙
ÍÍ
˙˙
ÍÍ 1
6
5
˙˙
Í
c. ÍÍ
˙
ÍÍÍ −7 −5 −8 ˙˙˙
Î
˚
ÈÍ
˘˙
ÍÍ
˙˙
Í 1 6 5 ˙˙
˙˙
d. ÍÍÍÍ
˙
ÍÍÍ 1 3 0 ˙˙˙
Î
˚
Which matrix expression produces the vertex
matrix for P ′Q ′R ′?
ÈÍ
Í
1 ÍÍÍÍ −2
2 ÍÍÍÍ
ÍÎ −2
ÈÍ
ÍÍ
Í −2
2 ÍÍÍÍ
ÍÍ
ÍÎ −2
ÈÍ
Í
1 ÍÍÍÍ −4
2 ÍÍÍÍ
ÍÎ −4
ÈÍ
ÍÍ
Í −4
2 ÍÍÍÍ
ÍÍ
ÍÎ −4
ÈÍ
ÍÍ
Í −2
JKL is ÍÍÍÍ
ÍÍ
ÍÎ 1
˘˙
˙
3 ˙˙˙˙
˙˙
˙
4 −3 ˙˙˚
˘˙
˙
2
3 ˙˙˙˙
˙˙
˙
4 −3 ˙˙˚
˘˙
˙
4
6 ˙˙˙˙
˙˙
˙
8 −6 ˙˙˚
˘˙
˙
4
6 ˙˙˙˙
˙˙
˙
8 −6 ˙˙˚
2
23
Name: ________________________
ID: Practice
ÈÍ
˘˙
ÍÍ
˙˙
ÍÍ 5 0
˙˙
8
Í
˙˙ .
117. The vertex matrix for MNO is ÍÍ
˙˙
ÍÍ
ÍÎ −3 2 −4 ˙˙˚
What is the vertex matrix for M ′N ′O ′, the image
produced by reflecting MNO over the x-axis?
ÈÍ
˘˙
ÍÍ
˙
ÍÍ 5 0
8 ˙˙˙˙
a. ÍÍÍ
˙˙
ÍÍ
˙
ÍÎ −3 2 −4 ˙˙˚
ÈÍ
˘˙
ÍÍ
˙
ÍÍ 5
0 8 ˙˙˙˙
b. ÍÍÍ
˙˙
ÍÍ
˙
ÍÎ 3 −2 4 ˙˙˚
ÈÍ
˘˙
ÍÍ
˙
ÍÍ −5
0 −8 ˙˙˙˙
c. ÍÍÍ
˙˙
ÍÍ
˙
ÍÎ 3 −2
4 ˙˙˚
ÍÈÍ
˙˘
ÍÍ −5 0 −8 ˙˙˙
Í
˙˙
d. ÍÍÍ
˙˙
ÍÍ
˙
ÍÎ −3 2 −4 ˙˙˚
118. In the diagram below, R ′S ′T ′ is the image
produced by applying a transformation to RST .
Which matrix calculation will give the vertex
matrix for R ′S ′T ′?
ÈÍ
˘˙
ÍÍ
˙
ÍÍ 2 4 3 ˙˙˙
˙˙
a. 2 ÍÍÍ
˙˙
ÍÍ
ÍÎ 5 4 1 ˙˙˚
ÈÍ
˘˙
˙
ÍÍ
Í
1 ÍÍ 4 8 6 ˙˙˙˙
b.
˙˙˙
2 ÍÍÍÍ
ÍÎ 10 8 2 ˙˙˚
˙˘
ÍÈÍ
˙˘ ÍÈ
ÍÍ 2 2 2 ˙˙˙ ÍÍÍ 2 4 3 ˙˙˙
Í
˙˙
Í
˙
˙˙ + ÍÍ
c. ÍÍÍ
˙˙
˙
ÍÍ
˙˙˙ ÍÍÍ
ÍÎ 2 2 2 ˙˚ ÍÎ 5 4 1 ˙˙˚
ÍÈÍ
˙˘
ÍÍ 1 1 1 ˙˙˙ È
˘
ÍÍ
˙˙ ÍÍ
ÍÍ
˙˙ ÍÍ 4 8 6 ˙˙˙˙
2
2
2
Í
˙
˙˙
˙˙ + ÍÍÍ
d. ÍÍÍ
˙˙
ÍÍ
˙˙˙ ÍÍÍ
ÍÍ 1 1 1 ˙˙ ÍÎ 10 8 2 ˙˙˙˚
ÍÍ
˙
ÍÍÎ 2 2 2 ˙˙˙˚
24
Name: ________________________
ID: Practice
NOP has vertices N ÁÊË 2,3 ˜ˆ¯ , O ÁÊË −1,4 ˜ˆ¯ , and
P ÊÁË 3,−5 ˆ˜¯ . Which matrix calculation is used to
determine the vertex matrix for the image
N ′O ′P ′ produced by a reflection across the
y-axis?
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙Í
˙
ÍÍ −1 0 ˙˙˙ ÍÍÍ 2 −1
3 ˙˙˙˙
˙˙ ÍÍ
a. ÍÍÍ
˙˙
˙˙ ÍÍ
ÍÍ
˙
4 −5 ˙˙˚
ÍÎ 0 1 ˙˙˚ ÍÍÎ 3
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙˙ ÍÍ
˙
ÍÍ 1
˙
Í
0 ˙˙ ÍÍ 2 −1
3 ˙˙˙˙
b. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙Í
˙
4 −5 ˙˙˚
ÍÎ 0 −1 ˙˙˚ ÍÍÎ 3
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙˙ ÍÍ
˙
ÍÍ −1
˙
Í
3 ˙˙˙˙
0 ˙˙ ÍÍ 2 −1
c. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙Í
˙
ÍÎ 0 −1 ˙˙˚ ÍÍÎ 3
4 −5 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙Í
˙
ÍÍ 0 1 ˙˙˙ ÍÍÍ 2 −1
3 ˙˙˙˙
˙˙ ÍÍ
d. ÍÍÍ
˙˙
˙˙ ÍÍ
ÍÍ
˙
ÍÎ 1 0 ˙˙˚ ÍÍÎ 3
4 −5 ˙˙˚
120.
DEF is reflected across the line y = x.
121.
119.
Triangle MRT has vertices at M ÊÁË 3,8 ˆ˜¯ , R ÊÁË 7,−2 ˆ˜¯ ,
and T ÊÁË −5,−4 ˆ˜¯ . If the triangle is to be translated by
the rule ÁÊË x ′,y ′ ˜ˆ¯ = ÁÊË x + 3,y − 2 ˜ˆ¯ , which matirx
expression models the translation?
ÈÍ
˘˙ ÈÍ
˘˙
˙˙ ÍÍ
ÍÍ
˙˙
˙˙ ÍÍ 3
ÍÍ 3
˙˙
7
−
5
3
3
˙
Í
Í
˙˙
a. ÍÍ
˙˙ + ÍÍ
˙˙
˙˙ ÍÍ
ÍÍ
ÍÎ 8 −2 −4 ˙˚ ÍÎ −2 −2 −2 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
˙˙ ÍÍ
ÍÍ
˙
˙˙ ÍÍ −2 −2 −2 ˙˙˙
ÍÍ 3
7
−
5
˙
Í
Í
˙˙
b. ÍÍ
˙˙ − ÍÍ
˙˙
˙˙ ÍÍ
ÍÍ
ÍÎ 8 −2 −4 ˙˚ ÍÎ 3
3
3 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
˙˙ ÍÍ
ÍÍ
˙
˙˙ ÍÍ −2 −2 −2 ˙˙˙
ÍÍ 3
7
−
5
˙
Í
Í
˙˙
c. ÍÍ
˙˙ + ÍÍ
˙˙
˙˙ ÍÍ
ÍÍ
ÍÎ 8 −2 −4 ˙˚ ÍÎ 3
3
3 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
˙˙˙ ÍÍÍ 3
ÍÍÍ 3
˙˙˙
7
−
5
3
3
˙˙ − ÍÍ
˙˙
d. ÍÍÍÍ
˙˙ ÍÍ
˙˙
˙˙ ÍÍ
ÍÍ
˙
ÍÎ 8 −2 −4 ˙˚ ÍÎ −2 −2 −2 ˙˙˚
Which matrix multiplication shows how to find
D ′E ′ F ′ ?
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙Í
˙
ÍÍ 1 0 ˙˙˙ ÍÍÍ 4 5 6 ˙˙˙
˙˙ ÍÍ
˙˙
a. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙
Í
ÍÎ 0 1 ˙˚ ÍÎ 1 3 1 ˙˙˚
ÍÈÍ
˙˘ ÍÈ
˙˘
ÍÍ 0 1 ˙˙˙ ÍÍÍ 4 5 6 ˙˙˙
Í
˙
Í
˙˙
˙˙ ÍÍ
b. ÍÍÍ
˙˙
ÍÍ
˙˙˙ ÍÍÍ
˙
ÍÎ 1 0 ˙˚ ÍÎ 1 3 1 ˙˙˚
ÍÈÍ
˙˘˙ ÍÈÍ
˙˘
ÍÍ −1
˙˙ ÍÍ 4 5 6 ˙˙˙
0
Í
˙
Í
˙˙
˙˙ ÍÍ
c. ÍÍÍ
˙˙
ÍÍ
˙˙˙ ÍÍÍ
˙
ÍÎ 0 −1 ˙˚ ÍÎ 1 3 1 ˙˙˚
ÍÈÍ
˙˘ ÍÈ
˙˘
ÍÍ 0 −1 ˙˙˙ ÍÍÍ 4 5 6 ˙˙˙
Í
˙
Í
˙˙
˙˙ ÍÍ
d. ÍÍÍ
˙˙
ÍÍ
˙˙˙ ÍÍÍ
˙
ÍÎ −1
0 ˙˚ ÍÎ 1 3 1 ˙˙˚
25
Name: ________________________
ID: Practice
122.
124.
Which matrix calculation was used to transform
STU to S ′T ′U ′?
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙Í
˙
ÍÍ 0 −1 ˙˙˙ ÍÍÍ −7 −4 −3 ˙˙˙
˙˙ ÍÍ
˙˙
a. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙
Í
0 ˙˚ ÍÎ 0
2
8 ˙˙˚
ÎÍ 1
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙˙ ÍÍ
˙
ÍÍ −1
˙
Í
0 ˙˙ ÍÍ −7 −4 −3 ˙˙˙˙
b. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙Í
˙
ÍÎ 0 −1 ˙˙˚ ÍÍÎ 0
2
8 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙Í
˙
ÍÍ −1 0 ˙˙˙ ÍÍÍ −7 −4 −3 ˙˙˙
˙˙ ÍÍ
˙˙
c. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙
Í
ÍÎ 0 1 ˙˚ ÍÎ 0
2
8 ˙˙˚
ÈÍ
˙˘˙ ÍÈÍ
˙˘˙
ÍÍ
ÍÍ 0 −1 ˙˙˙ ÍÍÍ −7 −4 −3 ˙˙˙
˙˙ ÍÍ
˙˙
d. ÍÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙
Í
ÍÎ −1
0 ˙˚ ÍÎ 0
2
8 ˙˙˚
ÈÍ
˘˙
˙
ÍÍÍ −2 3
3 ˙˙˙˙
123.
GHJ with vertex matrix ÍÍÍÍ
˙˙ is
ÍÍ
˙
ÍÎ 4 6 −2 ˙˙˚
1
dilated by a factor of . In the image G ′H ′J ′,
3
what are the coordinates of the vertex that lies in
the second quadrant?
ÊÁ 7 13 ˆ˜
a. ÁÁÁÁ − , ˜˜˜˜
Ë 3 3 ¯
ÊÁ 2 4 ˆ˜
b. ÁÁÁÁ − , ˜˜˜˜
Ë 3 3¯
ÊÁ
2 ˆ˜
c. ÁÁÁÁ 1,− ˜˜˜˜
3¯
Ë
Ê
ˆ
d. ÁË 1,2 ˜¯
125.
26
The vertices of quadrilateral GHIJ are G ÊÁË −1,−1 ˆ˜¯ ,
H ÁÊË 3,−2 ˜ˆ¯ , I ÁÊË 2,4 ˜ˆ¯ , and J ÁÊË −2,3 ˜ˆ¯ . G ′H ′I ′J ′ is the
image produced by translating quadrilateral GHIJ 6
units to the left. Which matrix represents
G ′H ′I ′J ′ ?
ÈÍ
˘˙
˙
ÍÍ
ÍÍ −7 −3 −4 −8 ˙˙˙
˙˙
a. ÍÍÍ
˙˙
ÍÍ
ÍÎ −7 −8 −2 −3 ˙˙˚
ÈÍ
˘˙
˙
ÍÍ
ÍÍ −7 −3 −4 −8 ˙˙˙
˙˙
b. ÍÍÍ
˙˙
ÍÍ
ÍÎ −1 −2
4
3 ˙˙˚
˙˘˙
ÍÈÍ
˙˙
ÍÍ −1
3
2
−2
˙˙
Í
c. ÍÍÍ
˙˙
˙
ÍÍ
ÍÎ −7 −8 −2 −3 ˙˙˚
˙˘˙
ÍÈÍ
˙˙
ÍÍ 5
9
8
4
˙˙
Í
d. ÍÍÍ
˙˙
˙
ÍÍ
ÍÎ −1 −2 4 3 ˙˙˚
M ′N ′O ′ is the image of MNO produced by
translating 3 units left and 1 unit up. The vertex
ÈÍ
˘˙
ÍÍ
˙˙
ÍÍ −1 2
˙˙
4
Í
˙˙ . Which is
′
′
′
matrix for M N O is ÍÍ
˙
ÍÍÍ 1 6 −3 ˙˙˙
Î
˚
the vertex matrix for MNO?
ÈÍ
˘˙
ÍÍ
˙
ÍÍ 2 5
7 ˙˙˙˙
a. ÍÍÍ
˙˙
ÍÍ
˙
ÍÎ 0 5 −4 ˙˙˚
ÈÍ
˘˙
˙
ÍÍ
ÍÍ −4 −1
1 ˙˙˙˙
b. ÍÍÍ
˙˙
˙
ÍÍ
ÍÎ 2
7 −2 ˙˙˚
ÈÍ
˘˙
ÍÍ
˙
ÍÍ −2 1 3 ˙˙˙
˙˙
c. ÍÍÍ
˙˙
ÍÍ
ÍÎ 4 9 0 ˙˙˚
ÈÍ
˘˙
˙
ÍÍ
ÍÍ 0 3
5 ˙˙˙˙
d. ÍÍÍ
˙˙
˙
ÍÍ
ÍÎ −2 3 −6 ˙˙˚
Name: ________________________
ID: Practice
126.
Polygon FGHI is represented by vertex matrix M .
ÈÍ
˘˙
˙
ÍÍÍ 2
4
4
2 ˙˙˙˙
M = ÍÍÍÍ
˙˙
ÍÍ
˙
ÍÎ −2 −2 −5 −5 ˙˙˚
Which multiplication would be used to reflect
polygon FGHI across the x − axis?
ÍÈÍ
˙˘˙ ÍÈÍ
˙˘˙
ÍÍ 1
˙˙ ÍÍ 2
˙˙
0
4
4
2
Í
˙
Í
˙˙
˙˙ ÍÍ
a. ÍÍÍ
˙˙
ÍÍ
˙˙˙ ÍÍÍ
˙
ÍÎ 0 −1 ˙˚ ÍÎ −2 −2 −5 −5 ˙˙˚
ÍÈÍ
˙˘ ÍÈ
˙˘˙
ÍÍ −1 0 ˙˙˙ ÍÍÍ 2
˙˙
4
4
2
Í
˙
Í
˙˙
˙˙ ÍÍ
b. ÍÍÍ
˙˙
ÍÍ
˙˙˙ ÍÍÍ
˙
ÍÎ 0 1 ˙˚ ÍÎ −2 −2 −5 −5 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙˙ ÍÍ
˙˙
ÍÍ −1
˙˙ ÍÍ 2
˙˙
0
4
4
2
Í
˙
Í
˙˙
c. ÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙˙ ÍÍ
ÍÎ 0 −1 ˙˚ ÍÎ −2 −2 −5 −5 ˙˙˚
ÈÍ
˘˙ ÈÍ
˘˙
ÍÍ
˙Í
˙˙
ÍÍ 0 −1 ˙˙˙ ÍÍÍ 2
˙˙
4
4
2
Í
˙
Í
˙˙
d. ÍÍ
˙˙ ÍÍ
˙˙
ÍÍ
˙˙ ÍÍ
ÍÎ −1
0 ˙˚ ÍÎ −2 −2 −5 −5 ˙˙˚
27