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}/_{3}x + 6?**

- (1) y=
^{1}/_{3}x + 15 - (2) y = – 3x – 15
- (3) y =
^{1}/_{3}x – 13 - (4) y = – 3x + 27

**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

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

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

Which quadrilateral best classifies ABCD?

- (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

- (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)

**Geometry 13 August 2014 Questions Answers Keys**

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