Geometry 19 June 2015 Questions Answer Keys

**The University of the State of New York**

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (2005 Standard)

Friday, June 19, 2015 — 1:15 to 4:15 p.m., only

Student Name:________________________________________________________

School Name: _________________________________________________________

**1. Quadrilateral ABCD undergoes a transformation, producing quadrilateral A’B’C’D’. For which transformation would the area of A’B’C’D’ not be equal to the area of ABCD?**

- (1) a rotation of 90° about the origin
- (2) a reflection over the y-axis
- (3) a dilation by a scale factor of 2
- (4) a translation defined by (x,y) → (x + 4,y – 1)

**2. The diameter of a sphere is 12 inches. What is the volume of the sphere to the nearest cubic inch?**

- (1) 288
- (2) 452
- (3) 905
- (4) 7,238

**3. A right rectangular prism is shown in the diagram below.**

Which line segments are coplanar?

**4. What are the coordinates of the image of point A(2,- 7) under the translation (x,y) → (x – 3,y + 5)?**

- (1) (- 1,- 2)
- (2) (- 1,2)
- (3) (5,- 12)
- (4) (5,12)

- (1) (6,10)
- (2) (- 6,4)
- (3) (- 8,- 4)
- (4) (18,16)

- (1) 20
- (2) 16
- (3) 12
- (4) 10

**7. 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 = – ½x + 5
- (2) y = – ½x + 4
- (3) y = 2x – 6
- (4) y = 2x

**8. In all isosceles triangles, the exterior angle of a base angle must always be**

- (1) a right angle
- (2) an acute angle
- (3) an obtuse angle
- (4) equal to the vertex angle

**9. If ΔW’X’Y is the image of ΔWXY after the transformation R _{90°}, which statement is false?**

**10. Which equation represents the circle shown in the graph below?**

- (1) (x – 2)² + y² = 9
- (2) (x + 2)² + y² = 9
- (3) (x – 2)² + y² = 3
- (4) (x + 2)² + y² = 3

**11. In quadrilateral ABCD, each diagonal bisects opposite angles. If m∠DAB = 70, then ABCD must be a**

- (1) rectangle
- (2) trapezoid
- (3) rhombus
- (4) square

**12. Which diagram illustrates a correct construction of an altitude of ΔABC?**

- (1) 33
- (2) 48
- (3) 57
- (4) 66

**14. Point A lies on plane P. How many distinct lines passing through point A are perpendicular to plane P ?**

- (1) 1
- (2) 2
- (3) 0
- (4) infinite

**15. Students made four statements about a circle.**

A: The coordinates of its center are (4,-3).

B: The coordinates of its center are (-4,3).

C: The length of its radius is 5√2.

D: The length of its radius is 25.

If the equation of the circle is (x + 4)² (y – 3)² = 50, which statements are correct?

- (1) A and C
- (2) A and D
- (3) B and C
- (4) B and D

**17. If ΔABC ∼ ΔLMN, which statement is not always true?**

**18. The equations representing lines k, m, and n are given below.**

k: 3y + 6 = 2x

m: 3y + 2x + 6 = 0

n: 2y = 3x + 6

Which statement is true?

- (1) k || m
- (2) n || m
- (3) m ⊥ k
- (4) m ⊥ n

**19. A regular polygon with an exterior angle of 40° is a**

- (1) pentagon
- (2) hexagon
- (3) nonagon
- (4) decagon

If MN = 8, ML = 5, and NL = 6, the perimeter of trapezoid BMNC is

- (1) 26
- (2) 28
- (3) 30
- (4) 35

**Geometry 19 June 2015 Questions Answers Keys**

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