# 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?

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

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)

What are the coordinates of point E?

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

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?

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?

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

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

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

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

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)
• (1) 20
• (2) 40
• (3) 60
• (4) 80

Which statement is always true based on the given information?

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}

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

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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