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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