# Geometry 28 January 2016

Geometry 28 January 2016 Questions Answer Keys

The University of the State of New York
The University Of The State Of New York
Regents High School Examination
Geometry
(Common Core)
Thursday, January 28, 2016 — 9:15 a.m. to 12:15 p.m., only

Student Name:________________________________________________________

School Name:________________________________________________________

1. William is drawing pictures of cross sections of the right circular cone below. Answer: (1)

2. An equation of a line perpendicular to the line represented by the equation y = – ½x – 5  and passing through (6, – 4) is

• (1) y = ½x + 4
• (2) y = ½x – 1
• (3) y = 2x + 14
• (4) y = 2x – 16
Answer: (4) y = 2x – 16 Answer: (3) 72°

4. A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank contains 1680 cubic inches of water. What percent of the fish tank is empty?

• (1) 10
• (2) 25
• (3) 50
• (4) 75
Answer: (2) 25

5. Which transformation would result in the perimeter of a triangle being different from the perimeter of its image?

• (1) (x,y) → (y,x)
• (2) (x,y) → (x,y)
• (3) (x,y) → (4x,4y)
• (4) (x,y) → (x + 2,y – 5)
Answer: (3) (x,y) → (4x,4y) Answer: (1)

7. As shown in the diagram below, a regular pyramid has a square base whose side measures 6 inches. If the altitude of the pyramid measures 12 inches, its volume, in cubic inches, is

• (1) 72
• (2) 144
• (3) 288
• (4) 432
Answer: (2) 144

8. Triangle ABC and triangle DEF are graphed on the set of axes below. Which sequence of transformations maps triangle ABC onto triangle DEF?

• (1) a reflection over the x-axis followed by a reflection over the y-axis
• (2) a 180º rotation about the origin followed by a reflection over the line y x
• (3) a 90º clockwise rotation about the origin followed by a reflection over the y-axis
• (4) a translation 8 units to the right and 1 unit up followed by a 90º counterclockwise rotation about the origin
Answer: (1) a reflection over the x-axis followed by a reflection over the y-axis

9. In Δ ABC, the complement of ∠B is ∠A. Which statement is always true?

• (1) tan ∠A tan ∠B
• (2) sin ∠A sin ∠B
• (3) cos ∠A tan ∠B
• (4) sin ∠A cos ∠B
Answer: (4) sin ∠A cos ∠B

10. A line that passes through the points whose coordinates are (1,1) and (5,7) is dilated by a scale factor of 3 and centered at the origin. The image of the line

• (1) is perpendicular to the original line
• (2) is parallel to the original line
• (3) passes through the origin
• (4) is the original line
Answer: (2) is parallel to the original line

11. Quadrilateral ABCD is graphed on the set of axes below. When ABCD is rotated 90° in a counterclockwise direction about the origin, its image is quadrilateral A’B’C’D. Is distance preserved under this rotation, and which coordinates are correct for the given vertex?

• (1) no and C'(1,2)
• (2) no and D'(2,4)
• (3) yes and A'(6,2)
• (4) yes and B'(3,4)
Answer: (4) yes and B'(–3,4)

12. In the diagram below of circle O, the area of the shaded sector LOM is 2π cm2. • (1) 10°
• (2) 20°
• (3) 40°
• (4) 80°
Answer: (3) 40°

13. In the diagram below, ABC ∼ DEF. If AB = 6 and AC = 8, which statement will justify similarity by SAS?

• (1) DE = 9, DF = 12, and ∠A ≅ ∠D
• (2) DE = 8, DF = 10, and ∠A ≅ ∠D
• (3) DE = 36, DF = 64, and ∠C ≅ ∠F
• (4) DE = 15, DF = 20, and ∠C ≅ ∠F
Answer: (3) DE = 36, DF = 64, and ∠C ≅ ∠F

14. The diameter of a basketball is approximately 9.5 inches and the diameter of a tennis ball is approximately 2.5 inches. The volume of the basketball is about how many times greater than the volume of the tennis ball?

• (1) 3591
• (2) 65
• (3) 55
• (4) 4
Answer: (3) 55

15. The endpoints of one side of a regular pentagon are (– 1,4) and (2,3). What is the perimeter of the pentagon?

• (1) √10
• (2) 5√10
• (3) 5√2
• (4) 25√2
Answer: (2) 5√10

16. In the diagram of right triangle ABC shown below, AB = 14 and AC = 9. What is the measure of ∠A, to the nearest degree?

• (1) 33
• (2) 40
• (3) 50
• (4) 57
Answer: (3) 50

17. What are the coordinates of the center and length of the radius of the circle whose equation is x2 + 6x + y2 – 4y = 23?

• (1) (3, –2) and 36
• (2) (3, –2) and 6
• (3) ( –3,2) and 36
• (4) ( –3,2) and 6
Answer: (4) ( –3,2) and 6

18. The coordinates of the vertices of Δ RST are R(– 2,– 3), S(8,2), and T(4,5). Which type of triangle is Δ RST?

• (1) right
• (2) acute
• (3) obtuse
• (4) equiangular
Answer: (1) right

19. Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere weighs .075 pound per cubic inch. If the sphere’s radius is 4 inches, what is the weight of the sphere, to the nearest pound?

• (1) 34
• (2) 20
• (3) 15
• (4) 4
Answer: (2) 20 Answer: (4) 20

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