Geometry 28 January 2015 Questions Answer Keys

**The University of the State of New York**

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (2005 Standard)

Wednesday, January 28, 2015 — 9:15 a.m. to 12:15 p.m., only

Student Name:________________________________________________________

School Name: _________________________________________________________

**1. What is the solution of the system of equations graphed below?**

y = 2x + 1

y = x² + 2x – 3

- (1) (0,- 3)
- (2) (- 1,- 4)
- (3) (- 3,0) and (1,0)
- (4) (- 2,- 3) and (2,5)

**2. What are the coordinates of the midpoint of the line segment with endpoints (2,-5) and (8,3)?**

- (1) (3,-4)
- (2) (3,-1)
- (3) (5,-4)
- (4) (5,-1)

**3. As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A’B’C’D’E’F’.**

Under this transformation, which property is not preserved?

- (1) area
- (2) distance
- (3) orientation
- (4) angle measure

If m∠A = 35, m∠ABD = 25, and m∠C = 60, which type of triangle is ΔBCD?

- (1) equilateral
- (2) scalene
- (3) obtuse
- (4) right

If AC = 18 and BD = 24, what is the length of one side of rhombus ABCD?

- (1) 15
- (2) 18
- (3) 24
- (4) 30

**6. What are the truth values of the statement “Opposite angles of a trapezoid are always congruent” and its negation?**

- (1) The statement is true and its negation is true.
- (2) The statement is true and its negation is false.
- (3) The statement is false and its negation is true.
- (4) The statement is false and its negation is false.

**7. What is the length of a line segment whose endpoints have coordinates (5,3) and (1,6)?**

- (1) 5
- (2) 25
- (3) √17
- (4) √29

- (1) 50
- (2) 80
- (3) 100
- (4) 130

Which statement must always be true for this construction?

**10. In ΔABC, AB = 4, BC = 7, and AC = 10. Which statement is true?**

- (1) m∠B m∠C m∠A
- (2) m∠B m∠A m∠C
- (3) m∠C m∠B m∠A
- (4) m∠C m∠A m∠B

**11. A circle whose center has coordinates (-3,4) passes through the origin. What is the equation of the circle?**

- (1) (x + 3)² (y – 4)² = 5
- (2) (x + 3)² (y – 4)² = 25
- (3) (x – 3)² (y + 4)² = 5
- (4) (x – 3)² (y + 4)² = 25

**12. Point W is located in plane R . How many distinct lines passing through point W are perpendicular to plane R ?**

- (1) one
- (2) two
- (3) zero
- (4) infinite

**13. In the diagram below, line is parallel to line m, and line w is a transversal.**

If m∠2 = 3x + 17 and m∠3 = 5x – 21, what is m∠1?

- (1) 19
- (2) 23
- (3) 74
- (4) 86

**14. The diagram below is a graph of circle O.**

Which equation represents circle O?

- (1) (x – 5)² (y + 3)² = 4
- (2) (x + 5)² (y – 3)² = 4
- (3) (x – 5)² (y + 3)² = 16
- (4) (x + 5)² (y – 3)² = 16

If m∠Q = 5x + 3 and m∠R = 7x – 15, what is m∠Q?

- (1) 83
- (2) 48
- (3) 16
- (4) 9

**16. Triangle ABC is graphed on the set of axes below.**

What are the coordinates of the point of intersection of the medians of ΔABC?

- (1) (-1,2)
- (2) (-3,2)
- (3) (0,2)
- (4) (1,2)

**17. Given the statement, “If a number has exactly two factors, it is a prime number,” what is the contrapositive of this statement?**

- (1) If a number does not have exactly two factors, then it is not a prime number.
- (2) If a number is not a prime number, then it does not have exactly two factors.
- (3) If a number is a prime number, then it has exactly two factors.
- (4) A number is a prime number if it has exactly two factors.

**18. Which graph represents a circle whose equation is (x – 2)² + (y + 4)² = 4?**

**19. If two sides of a triangle have lengths of 4 and 10, the third side could be**

- (1) 8
- (2) 2
- (3) 16
- (4) 4

**20. The lines represented by the equations 4x + 6y = 6 and y = ^{2}/_{3} x – 1 are**

- (1) parallel
- (2) the same line
- (3) perpendicular
- (4) intersecting, but not perpendicular

**Geometry 28 January 2015 Questions Answers Keys**

Geometry Examination Question |

Scoring Key and Rating Guide |

**See also: **