Geometry 13 August 2014

Geometry 13 August 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Wednesday, August 13, 2014 — 8:30 to 11:30 a.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

1. A rectangular prism is shown in the diagram below.

Which pair of line segments would always be both congruent and parallel?

Answer: (4)  
Answer: (3)  
Answer: (4)  

4. What is an equation of the line that passes through (- 9,12) and is perpendicular to the line whose equation is y = 1/3x + 6?

  • (1) y=1/3x + 15
  • (2) y = – 3x – 15
  • (3) y =1/3x – 13
  • (4) y = – 3x + 27
Answer: (2) y = – 3x – 15

5. In the diagram below, under which transformation is ΔX’Y’Z’ the computations. image of ΔXYZ?

  • (1) dilation
  • (2) reflection
  • (3) rotation
  • (4) translation
Answer: (3) rotation

6. What is the solution of the system of equations y – x = 5 and y = x² + 5?

  • (1) (0,5) and (1,6)
  • (2) (0,5) and (- 1,6)
  • (3) (2,9) and (- 1,4)
  • (4) (- 2,9) and (- 1,4)
Answer: (1) (0,5) and (1,6)

What are the coordinates of point E?

  • (1) (0.5,2)
  • (2) (4.5,2)
  • (3) (5.5,5)
  • (4) (7.5,7)
Answer: (3) (5.5,5)

8. Right triangle ABC is shown in the graph below.

After a reflection over the y-axis, the image of ΔABC is A’B’C’. Which statement is not true?

Answer: (4)  

9. What is an equation of circle O shown in the graph below?

  • (1) (x – 2)² + (y + 4)² = 4
  • (2) (x – 2)² + (y + 4)² = 16
  • (3) (x + 2)² + (y – 4)² = 4
  • (4) (x + 2)² + (y – 4)² = 16
Answer: (4) (x + 2)² + (y – 4)² = 16

Which proportion would always represent a correct relationship of the segments?

Answer: (3)  

11. Quadrilateral ABCD is graphed on the set of axes below.

Which quadrilateral best classifies ABCD?

  • (1) trapezoid
  • (2) rectangle
  • (3) rhombus
  • (4) square
Answer: (3) rhombus

12. Circle O is represented by the equation (x + 3)² + (y – 5)² = 48. The coordinates of the center and the length of the radius of circle O are

  • (1) ( – 3,5) and 4√3
  • (2) ( – 3,5) and 24
  • (3) (3,- 5) and 4√3
  • (4) (3,- 5) and 24
Answer: (1) ( – 3,5) and 4√3 
  • (1) parallel chords intercept congruent arcs
  • (2) congruent chords intercept congruent arcs
  • (3) if two chords are parallel, then they are congruent
  • (4) if two chords are equidistant from the center, then the arcs they intercept are congruent
Answer: (1)  

14. What is the slope of a line perpendicular to the line whose equation is 3x – 7y + 14 = 0?

  • (1) 3/7
  • (2) – 3/7
  • (3) 3
  • (4) 1/3
Answer: (2) – 3/7

15. Line segment AB has endpoint A located at the origin. Line segment AB is longest when the coordinates of B are

  • (1) (3,7)
  • (2) (2,- 8)
  • (3) (- 6,4)
  • (4) (- 5,- 5)
Answer: (2) (2,- 8)
  • (1) 20
  • (2) 40
  • (3) 60
  • (4) 80
Answer: (3) 60
 

Which statement is always true based on the given information?

Answer: (4)  

18. Which set of numbers could represent the lengths of the sides of a right triangle?

  • (1) {2, 3, 4}
  • (2) {5, 9, 13}
  • (3) {7, 7, 12}
  • (4) {8, 15, 17}
Answer: (4) {8, 15, 17}

19. In quadrilateral ABCD, the diagonals bisect its angles. If the diagonals are not congruent, quadrilateral ABCD must be a

  • (1) square
  • (2) rectangle
  • (3) rhombus
  • (4) trapezoid
Answer: (3) rhombus

20. Line m and point P are shown in the graph below.

Which equation represents the line passing through P and parallel to line m?

  • (1) y – 3 = 2(x + 2)
  • (2) y + 2 = 2(x – 3)
  • (3) y – 3 = – ½ (x + 2)
  • (4) y + 2 = – ½ (x – 3)
Answer: (2) y + 2 = 2(x – 3)

Geometry 13 August 2014 Questions Answers Keys

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