Name: ____________________________________
Geometry Honors Take Home
1. Point A (4, 7) and point B ( -6, 1) are endpoints of Point C is the midpoint of perpendicular to 1. 3x −​ 5y = 17
2. 3x +​ 5​ y = 17
3. 5x − 3y = 7
4. 5x + 3y = 7
.
5. Which pair of edges is not coplanar in the cube shown
below?
. What is the equation of a line
that passes through point C?
2. In the diagram below of ΔABC, point H is the intersection of
the three medians.
If measures 2.4 centimeters, what is the length, in
centimeters, of ?
1. 3.6 3. 7.2
2. 4.8 4. 9.6
3. A carpenter made a storage container in the shape of a
rectangular prism. It is 5 feet high and has a volume of 720 cubic
feet. He wants to make a second container with the same height
and volume as the first one, but in the shape of a triangular
prism. What will be the number of square feet in the area of the
base of the new container?
1. 36 3. 144
2. 72 4. 288
4. What is an equation of the line that passes through the point
(−2, 1) and is parallel to the line whose equation is 4x − 2y = 8?
1. y = x + 2
2. y = x − 2
3. y = 2x + 5
4. y = 2x − 5
1. 2. 3. and and and 4. and 6. Triangle JTM is shown on the graph below.
Which transformation would result in an image that is not congruent to ΔJTM?
1. 2. 3. 4. ry = x
R90°
T0,−3
D2
7. What are the coordinates of P′, the image of point P(x, y) after translation T4, 4?
1. 2. 3. 4. (x − 4, y − 4)
(x + 4, y + 4)
(4x, 4y)
(4, 4)
8. Use the diagram below to answer the question.
What is the ratio of the length of to the length of ?
1. 1 : 4 3. 3 : 1
2. 2 : 3 4. 3 : 5
9. What is an equation of the line that passes through the point (4, 5) and is parallel to the line whose equation is y = 1. 2. 3. 4. 2y + 3x = 11
2y + 3x = 22
3y - 2x = 2
3y - 2x = 7
x - 4?
10. In the diagram below of ∆MAR, medians , 13. Point M is the midpoint of . If the coordinates of M are
(2, 8) and the coordinates of A are (10, 12), what are the
coordinates of B?
1. (6, 10) 3. (-8, -4)
2. (-6, 4) 4. (18, 16)
, and intersect at O.
14. What are the coordinates of the image of point A (2, -7)
under the translation (x, y) → (x - 3, y + 5)?
1. (-1, -2) 3. (5, -12)
2. (-1, 2) 4. (5, 12)
15. A right rectangular prism is shown in the diagram below.
If TO = 10, what is the length of ?
1. 30 3. 20
2. 25 4. 15
11. In the prism shown below, ⊥ and ⊥ .
Which line segments are coplanar?
Which plane is perpendicular to ?
1. HEA 3. EAB
2. BAD 4. EHG
12. What is an equation of the line that passes through the
point (2, 4) and is perpendicular to the line whose equation is 3y
= 6x + 3?
1. y = -
x + 5
2. y = -
x + 4
3. y = 2x - 6
4. y = 2x
1. and 2. 3. 4. and and and 16. The diameter of a sphere is 12 inches. What is the volume
of the sphere to the nearest cubic inch?
1. 288 3. 905
2. 452 4. 7,238
17. As shown in the diagram below, E, and || .
and Given ∆AEC ~ ∆BED, which equation is true?
1. 2. 3. 4. intersect at
18. In the diagram below, which single transformation was used
to map triangle A onto triangle B?
1. line reflection 3. dilation
2. rotation
4. translation
19. Given shown below, with M(-6, 1) and N(3, -5), what is
an equation of the line that passes through point P(6, 1) and is
parallel to ?
1. y = -
x + 5
2. y = -
x - 3
3. y = x + 7
4. y = x - 8
20. A sequence of transformations maps rectangle ABCD onto
rectangle A”B”C”D”, as shown in the diagram below.
Which sequence of transformations maps ABCD onto A’B’C’D’
and then maps A’B’C’D’ onto A”B”C”D”?
1. 2. 3. 4. a reflection followed by a rotation
a reflection followed by a translation
a translation followed by a rotation
a translation followed by a reflection
21. In the diagram below, a square is graphed in the coordinate
plane.
23. Triangles ABC and DEF are drawn below.
If AB = 9, BC = 15, DE = 6, EF = 10, and ∠B ≅ ∠E, which
statement is true?
1. ∠CAB ​≅ ∠DEF
2. 3. ∆ABC ~ ∆DEF
A reflection over which line does not carry the square onto
itself?
1. 2. 3. 4. x = 5
y = 2
y = x
x + y = 4
22. If the rectangle below is continuously rotated about side w,
which solid figure is formed?
1. pyramid
3. cone
2. rectangular prism 4. cylinder
4. 24. Which figure can have the same cross section as a sphere?
25. In the diagram below, congruent figures 1, 2, and 3 are
drawn.
1. 2. 3. Which sequence of transformations maps figure 1 onto figure 2
and then figure 2 onto figure 3?
1. 2. 3. 4. a reflection followed by a translation
a rotation followed by a translation
a translation followed by a reflection
a translation followed by a rotation
26. Which object is formed when right triangle RST shown
below is rotated around leg ?
4. 1. 2. 3. 4. a pyramid with a square base
an isosceles triangle
a right triangle
a cone
27. In the diagram below, a right circular cone with a radius of 3
inches has a slant height of 5 inches, and a right cylinder with a
radius of 4 inches has a height of 6 inches.
29. The slope of ⊥ is and the slope of is . If , find the value of x.
1. 2. 2
3. 6
4. 30. Write an equation of a line that is parallel to the line whose
equation is 3y = x + 6 and that passes through the point (-3, 4).
1. y = How many full cones of water is needed to completely fill the
cylinder with water?
1. 8 3. 12
2. 16 4. 10
x + 4
2. y - 4 = (x + 3)
3. y + 4 = -
(x - 3)
4. y = -3x + 2
28. Quadrilateral HYPE has vertices H(2,3), Y(1,7), P(-2,7), and
E(-2,4). State and label the coordinates of the vertices of P′′ after
the composition of transformations rx-axis ° T5,-3.
1. (3, -4) 3. (3, 10)
2. (-3, 4) 4. (3, -10)
31. Given:
and ≅ ≅ and intersect at point C
are drawn
Which of the following is the correct way to prove ΔABC ≅
ΔDEC?
1. Hypotenuse, Leg 3. Side, Angle, Side
2. Angle, Side, Angle 4. Side, Side, Side
32. For which diagram is the statement ΔABC ∼ ΔADE not
always true?
33. In the diagram below, which transformation?
is the image of under
1. 2. 3. 4. 1. dilation 3. translation
2. reflection 4. glide reflection
34. Triangle A′B′C′ is the image of ΔABC after a dilation of 2.
Which statement is true?
1. AB = A′B′
2. BC = 2(B′C′)
3. m∠B = m∠B′
4. m∠A = (m∠A′)
35. Triangle ABC is graphed on the set of axes below.
38. A regular pyramid has a height of 12 centimeters and a
square base. If the volume of the pyramid is 256 cubic
centimeters, how many centimeters are in the length of one
side of its base?
1. 8 3. 32
2. 16 4. 64
39. Line m and point P are shown in the graph below.
What are the coordinates of the point of intersection of the
medians of ΔABC?
1. (-1,2) 3. (0,2)
2. (-3,2) 4. (1,2)
36. What is the length of a line segment whose endpoints have
coordinates (5,3) and (1,6)?
1. 5
2. 25
3. Which equation represents the line passing through P and
parallel to line m?
1. y – 3 = 2(x + 2)
2. y + 2 = 2(x – 3)
3. y – 3 = –
(x + 2)
4. y + 2 = –
(x – 3)
4. 37. What are the coordinates of the midpoint of the line segment
with endpoints (2, -5) and (8, 3)?
1. (3, -4) 3. (5, -4)
2. (3, -1) 4. (5, -1)
40. As shown in the diagram below, a landscaper uses a cylindrical lawn roller on a lawn. The roller has a radius of 9 inches and a
width of 42 inches.
To the nearest square inch, the area the roller covers in one complete rotation is
1. 2,374 3. 10,682
2. 2,375 4. 10,688