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.**

**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

**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

**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)

**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

**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

**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

**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

**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)

**12. In the diagram below of circle O, the area of the shaded sector LOM is 2π cm ^{2}.**

- (1) 10°
- (2) 20°
- (3) 40°
- (4) 80°

**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

**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

**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

**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

**17. What are the coordinates of the center and length of the radius of the circle whose equation is x ^{2} + 6x + y^{2} – 4y = 23?**

- (1) (3, –2) and 36
- (2) (3, –2) and 6
- (3) ( –3,2) and 36
- (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

**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

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