# Geometry 26 January 2016

Geometry 26 January 2016 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Tuesday, January 26, 2016 — 1:15 to 4:15 p.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

1. What is the equation of a circle with its center at (5,–2) and a radius of 3?

• (1) (x – 5)2 + (y + 2)2 = 3
• (2) (x – 5)2 + (y + 2)2 = 9
• (3) (x + 5)2 + (y – 2)2 = 3
• (4) (x + 5)2 + (y – 2)2 = 9
Answer: (2) (x – 5)2 + (y + 2)2 = 9

2. In the diagram below, ∠ABC is inscribed in circle O.  • (1) 1:1
• (2) 1:2
• (3) 1:3
• (4) 1:4
Answer: (2) 1:2   • (1) 8
• (2) 2
• (3) 16
• (4) 32
Answer: (3) 16

4. How many points are 3 units from the origin and also equidistant from both the x-axis and y-axis?

• (1) 1
• (2) 2
• (3) 0
• (4) 4
Answer: (4) 4

5. The converse of the statement “If a triangle has one right angle, the triangle has two acute angles” is

• (1) If a triangle has two acute angles, the triangle has one right angle.
• (2) If a triangle has one right angle, the triangle does not have two acute angles.
• (3) If a triangle does not have one right angle, the triangle does not have two acute angles.
• (4) If a triangle does not have two acute angles, the triangle does not have one right angle.
Answer: (1) If a triangle has two acute angles, the triangle has one right angle.

6. The surface area of a sphere is 2304π square inches. The length of a radius of the sphere, in inches, is

• (1) 12
• (2) 24
• (3) 288
• (4) 576
Answer: (2) 24  Which statement is true?

• (1) AC > AB
• (2) AB > BC
• (3) BC < AC
• (4) AC < AB
Answer: (4) AC < AB  If LM = x + 7, ON = 3x + 11, and PQ = 25, what is the value of x?

• (1) 1.75
• (2) 3.5
• (3) 8
• (4) 17
Answer: (3) 8

9. Points A and B are on line ℓ. How many points are 3 units from line ℓ and also equidistant from A and B?

• (1) 1
• (2) 2
• (3) 3
• (4) 4
Answer: (2) 2

10. The lines whose equations are 2x + 3y = 4 and y = mx + 6 will be  perpendicular when m is Answer: (3)

11. As shown in the diagram below, M, R, and T are midpoints of the sides of ΔABC. If AB = 18, AC = 14, and BC = 10, what is the perimeter of quadrilateral ACRM?

• (1) 35
• (2) 32
• (3) 24
• (4) 21
Answer: (1) 35  If m∠HFG = 130 and m∠EHF = 70, what is m∠ABE?

• (1) 40
• (2) 50
• (3) 60
• (4) 70
Answer: (3) 60

13. The graphs of the lines represented by the equations y = 13x + 7 and y = –13x -2 are

• (1) parallel
• (2) horizontal
• (3) perpendicular
• (4) intersecting, but not perpendicular
Answer: (4) intersecting, but not perpendicular

14. Which graph represents a circle whose equation is (x + 3)² + (y – 1)² = 4? Answer: (1) • (1) 25
• (2) 30
• (3) 40
• (4) 46
Answer: (3) 40   Answer: (2)

17. When the transformation T2,1 is performed on point A, its image is point A'(- 3,4). What are the coordinates of A?

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

18. If the sum of the interior angles of a polygon is 1440º, then the polygon must be

• (1) an octagon
• (2) a decagon
• (3) a hexagon
• (4) a nonagon
Answer: (2) a decagon  If CR = 24 and RF = 2x – 6, what is the value of x?

• (1) 9
• (2) 12
• (3) 15
• (4) 27
Answer: (1) 9

20. Which equation represents a line that passes through the point (- 2,6) and is parallel to the line whose equation is 3x – 4y = 6?

• (1) 3x + 4y = 18
• (2) 4x + 3y = 10
• (3) – 3x + 4y = 30
• (4) – 4x + 3y = 26
Answer: (3) – 3x + 4y = 30

Geometry 26 January 2016 Questions Answers Keys Geometry Examination Question Scoring Key and Rating Guide

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