8th Grade – Domain 3: Geometry (28%)
1. XYZ was obtained from ABC by a rotation about the
point P.
(MGSE8.G.1)
Which indicates the correspondence of the vertices?
A.
A  X , B Y,C  Z
B.
A  Y, B  Z,C  X
C.
A  X , B  Z,C  Y
D. A  Z , B  X , C  Y
2. Rectangle ABCD is shown in the coordinate plane
below. Rectangle RVTS (not shown) has coordinates
R(0, 4), V(-9, 4), T(-9, 9), and S(0, 9). Which of the
following is true about rectangles ABCD and RVTS?
(MGSE8.G.1)
A. 𝐴𝐵𝐶𝐷 ≅ 𝑅𝑉𝑇𝑆 since the image when ABCD is
reflected over the y-axis is RVTS.
B. 𝐴𝐵𝐶𝐷 ≇ 𝑅𝑉𝑇𝑆 since the image when ABCD is
reflected over the y-axis is not RVTS.
C. 𝐴𝐵𝐶𝐷 ≅ 𝑅𝑉𝑇𝑆 since the image when ABCD is
rotated 90° counterclockwise about the origin is
RVTS.
D. 𝐴𝐵𝐶𝐷 ≇ 𝑅𝑉𝑇𝑆 since the image when ABCD is
rotated 90° counterclockwise about the origin is
not RVTS.
3. Vanessa is drawing some designs for her invitations.
She divides a grid into 4 quadrants and starts by
drawing a shape in one of the quadrants. Which shape
below shows the image of her design after a reflection
in the x-axis?
(MGSE8.G.1)
A.
B.
C.
D.
4. Which of the following transformation is not a rigid
motion?
(MGSE8.G.1)
A. Dilation
B. Reflection
C. Rotation
D. Translation
5. In the figure below, polygon RSTUV is the image of
ABCDE after a series of transformations. If the two
polygons are congruent, which side must have the
same length as side BC?
(MGSE8.G.2)
A. CD
B. DE
C. ST
D. TU
6. If figure 1 is rotated 90⁰ about the origin, line segment ̅̅̅̅
𝐶𝐷
would be congruent to which segment in figure 2?
(MGSE8.G.1, MGSE8.G.2)
A. ZW
B. XW
B
D
A
C
X
Y
W
Z
C. BC
D. AD
7. Trapezoid ABCD is shown on the coordinate grid
below. ABCD is translated to form A’B’C’D’ (not
shown), which is congruent to ABCD. If the coordinates
of D’ are (-1, 3), what is the rule for the translation
that maps ABCD onto A’B’C’D’?
(MCC.8.G.2)
A. (𝑥, 𝑦) → (𝑥 − 5, 𝑦 + 6)
B. (𝑥, 𝑦) → (𝑥 − 6, 𝑦 + 5)
C. (𝑥, 𝑦) → (𝑥 + 6, 𝑦 − 5)
D. (𝑥, 𝑦) → (𝑥 + 5, 𝑦 − 6)
8. Which of the following is not a transformations that proves
that shape G is congruent to shape H.
(MGSE8.G.2)
A. Reflect shape G across the x-axis then translate it 6
units right.
B.
Reflect shape G across the y-axis then reflect it across
the x-axis.
C.
Rotate shape G 180⁰ about the origin
D. Rotate shape G 180 about the origin and reflect over
the y-axis.
9. ∆𝐴𝐵𝐶 is rotated 180° clockwise about the origin to
form ∆𝐷𝐸𝐹. What are the coordinate of the vertices
of ∆𝐷𝐸𝐹?
(MGSE8.G.3)
A. A’ (7, 4), B’ (4, 2), C’ (3, 8)
B. A’ (-4, 7), B’ (-2, 4), C’ (-8, 2)
C. A’ (4, -7), B’ (2, -4), C’ (2, -8)
D. (-7, 4), B’ (-4, 2), C’ (-3, 8)
10. Quadrilateral EFGH, shown in the coordinate plane
below, is dilated with the center at the origin to form
quadrilateral ABCD. What is the scale factor of the
dilation?
(MGSE8.G.3)
A.
B.
1
4
1
3
C. 3
D. 4
11. What are the coordinates of the image of point P(–3, –7)
after a reflection about the line y = 2?
(MGSE8.G.3)
A. (–3, 9)
B. (–3, 11)
C. (5, –7)
D. (7, –7)
12. If Figure ABCD is translated so that the image of A is A' at
(−3,2), then the coordinates of the image of point B will
be…
(MGSE8.G.3)
A. (0,0)
B. (-1,4)
C. (-2,-1)
D. (-3,1)
13. An equilateral triangle with side lengths of 6 undergoes
dilation with a scale factor of 3:7. What are the side lengths
of the image?
(MGSE8.G.4)
A. X = 10
B. X = 12
C. X = 14
D. X = 16
14. Using transformations explain how you know that figure A
and figure B are similar.
(MGSE8.G.4)
A. Rotate figure A 90⁰ about the origin and all sides and
vertices correspond.
A
B. Rotate figure A 180⁰ about the origin and all sides and
vertices correspond.
C. Rotate figure A 270⁰ about the origin and all sides and
vertices correspond.
D. Rotate figure A 0⁰ about the origin and all sides and
vertices correspond.
15.
∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 are shown on this coordinate grid.
Describe a sequence of transformations that verify
that these triangles are geometrically similar.
(MGSE8.G.4)
16. Triangle BAD with vertices B(1, 1), A(3, 0), D(3, 3) is
translated 3 units to the left then reflected over the
x-axis. What are the coordinates of the image of the
original triangle after the transformations are
performed? Use the grid below to perform the
transformations.
(MGSE8.G.4)
A.
B.
C.
D.
B’ (-2, -1), A’ (0, 0), D’ (0, -3)
B’ (-2, 1), A’ (0, 0), D’ (0, 3)
B’ (1,, -2), A’ (0, 0), D’ (3, 0)
B’ (-1, -2), A’ (0, -3), D’ (0, 0)
B
17. Lines l and m are parallel to one another and cut by
transversals s and t.
(MGSE8.G.5)
What is the measure of angle x?
A. 40°
B. 80°
C. 120°
D. 140°
18. Right triangle ABC and right triangle ACD overlap as
shown below. Angle DAC measures 20° and angle BCA
measures 30°. What are the measures of angles x and
y? Explain.
(MGSE8.G.5)
19. Find the values of y and z.
A.
B.
C.
D.
𝑦 = 35°,
𝑦 = 37°,
𝑦 = 49°,
𝑦 = 55°,
(MGSE8.G.5)
𝑧 = 55°
𝑧 = 49°
𝑧 = 37°
𝑧 = 35°
20. If a and b are parallel lines that are cut by transversal
c, and m∠8 = 57°, what is the measure of ∠3?
(MGSE8.G.5)
A.
B.
C.
D.
57°
90°
123°
180°
MGSE8.G.7
21.Two sailboats leave Key Largo, Florida.
One of the sailboats travels 3 miles east
and then 4 miles north. The second
sailboat travels 8 miles south and 6
miles west.
How far apart in miles, are the boats.
A. 14 miles
B. 15 miles
C. 17 miles
D. 19 miles
MGSE8.G.7
22.
A can of drink is in the shape of a
cylinder with height 15 cm and radius 4
cm. What is the length of the longest
straw that will fit inside the can?
A. 17 cm
B. 19 cm
C. 21 cm
D. 23 cm
MGSE8.G.7
23. The distance between the bases on a
baseball diamond is 90 feet as shown to
the right: What is the distance (d), in
feet, between home plate and second
base? Round your answer to the nearest
whole number. (Use 1.414 for √𝟐)
A.
B.
C.
D.
90
127
135
180
MGSE8.G.7
24.The cube below has a length of 12 in.
What would be the length of a diagonal
along either of its faces?
A.
B.
C.
D.
12√2
14√2
24√2
48√2
𝑖𝑛𝑐ℎ𝑒𝑠
𝑖𝑛𝑐ℎ𝑒𝑠
𝑖𝑛𝑐ℎ𝑒𝑠
𝑖𝑛𝑐ℎ𝑒𝑠
MGSE8.G.9
25.What is the approximate volume of the
cone to the right? (Use 3.14 for 𝝅)
A.
B.
C.
D.
70 𝑐𝑚3
183 𝑐𝑚3
549 𝑐𝑚3
733 𝑐𝑚3
MGSE8.G.9
26.
The right cylinder has a radius of 3
inches and a height of 4 inches.
What is the approximate volume, in
cubic inches, of the cylinder?
A.
B.
C.
D.
12𝜋 𝑖𝑛3
36𝜋 𝑖𝑛3
48𝜋 𝑖𝑛3
60𝜋 𝑖𝑛3
MGSE8.G.9
27.The right cylinder and right cone shown
to the right have the same radius and
volume. The cylinder has a height of 12
inches. What is h, the height of the
cone?
A. 18 inches
B. 24 inches
C. 36 inches
D. 42 inches
MGSE8.G.9
28.Tawana has a spherical bottle shaped
like a basketball. Each cubic inch of the
bottle can hold 2 cups of water. If the
bottle is completely full, approximately
how many cups of water can it hold?
(Use 3.14 for 𝝅)
A.
B.
C.
D.
452 cups
904 cups
1808 cups
3616 cups
MGSE8.G.8
29.What is the approximate distance in
inches between the two endpoints of
the segment on the right?
A.
B.
C.
D.
1.4 inches
2.8 inches
7.1 inches
8.2 inches
MGSE8.G.8
30.Use your knowledge of the
Pythagorean Theorem to find the
approximate distance between 𝑃1 and
𝑃2 . Round your answer to the nearest
whole number.
A.
B.
C.
D.
7
9
12
17
MGSE8.G.8
31.Graph the points: (5, 5) and (-6, -4) on a
coordinate plane and calculate the
distance between them. Round your
answer to the nearest hundredth.
A.
B.
C.
D.
10.50
14.21
20.22
15.25
MGSE8.G.8
32.The segment to the right represents the
string that a fisherman used to measure
the length of an eel that got caught in
his net. What was the approximate
length (in feet) of the eel? Round your
answer to the nearest tenth?
A.
B.
C.
D.
7.6 feet
8.7 feet
9.4 feet
10.5 feet
MGSE8.G.6
33.Do 12, 5 and 13 represent the possible
side lengths of a right triangle? Explain.
A.
B.
C.
D.
Yes, because 5 + 12 > 13
Yes, because 52 + 122 = 132
No, because 52 + 122 ≠ 132
No, because 12 + 13 > 5
MGSE8.G.6
34.What kind of triangle is it when
𝑎2 + 𝑏 2 < 𝑐 2 ?
A.
B.
C.
D.
Right triangle
Obtuse triangle
Acute triangle
None of the above
MGSE8.G.6
35.The square to the right has a diagonal
of 15√2 inches, what is the perimeter
of the square?
A.
B.
C.
D.
30 inches
45 inches
60 inches
225 inches
MGSE8.G.6
36. 6, 9, 10 represent the side lengths of a
triangle. Is the triangle represented by
the given side lengths a right triangle?
Explain.
A.
B.
C.
D.
Yes, because 62 + 92 = 102
Yes, because 8 + 9 > 10
No, because 6 + 10 ≠ 13
No, because 62 + 92 ≠ 102