Geometry 19 June 2015

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)
Answer: (3) a dilation by a scale factor of 2

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
Answer: (3) 905

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

Which line segments are coplanar?

Answer: (4)

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)
Answer: (1) (- 1,- 2)
• (1) (6,10)
• (2) (- 6,4)
• (3) (- 8,- 4)
• (4) (18,16)
Answer: (2) (- 6,4)
• (1) 20
• (2) 16
• (3) 12
• (4) 10
Answer: (3) 12

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
Answer: (1) y = – ½x + 5

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
Answer: (3) an obtuse angle

9. If ΔW’X’Y is the image of ΔWXY after the transformation R90°, which statement is false?

Answer: (2)

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
Answer: (1) (x – 2)² + y² = 9

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
Answer: (3) rhombus

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

Answer: (2)
• (1) 33
• (2) 48
• (3) 57
• (4) 66
Answer: (2) 48

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
Answer: (1) 1

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
Answer: (3) B and C
Answer: (2)

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

Answer: (1)

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
Answer: (4) m ⊥ n

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

• (1) pentagon
• (2) hexagon
• (3) nonagon
• (4) decagon
Answer: (3) nonagon

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

• (1) 26
• (2) 28
• (3) 30
• (4) 35
Answer: (4) 35

Geometry 19 June 2015 Questions Answers Keys

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