# Geometry 28 January 2015

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)
Answer: (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)
Answer: (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
Answer: (3) orientation  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
Answer: (1) equilateral  If AC = 18 and BD = 24, what is the length of one side of rhombus ABCD?

• (1) 15
• (2) 18
• (3) 24
• (4) 30
Answer: (1) 15

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.
Answer: (3) The statement is false and its negation is true.

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
Answer: (1) 5  • (1) 50
• (2) 80
• (3) 100
• (4) 130
Answer: (4) 130  Which statement must always be true for this construction? Answer: (2)

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
Answer: (2) m∠B  m∠A  m∠C

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
Answer: (2) (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
Answer: (1) one

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
Answer: (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
Answer: (3) (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
Answer: (2) 48

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)
Answer: (1) (-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.
Answer: (2) If a number is not a prime number, then it does not have exactly two factors.

18. Which graph represents a circle whose equation is (x – 2)² + (y + 4)² = 4? Answer: (3)

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
Answer: (1) 8

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
Answer: (4) intersecting, but not perpendicular

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