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

**2. In the diagram below, ∠ABC is inscribed in circle O.**

- (1) 1:1
- (2) 1:2
- (3) 1:3
- (4) 1:4

- (1) 8
- (2) 2
- (3) 16
- (4) 32

**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

**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.

**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

Which statement is true?

- (1) AC > AB
- (2) AB > BC
- (3) BC < AC
- (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

**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

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

**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

If m∠HFG = 130 and m∠EHF = 70, what is m∠ABE?

- (1) 40
- (2) 50
- (3) 60
- (4) 70

**13. The graphs of the lines represented by the equations y = ^{1}⁄_{3}x + 7 and y = –^{1}⁄_{3}x -2 are**

- (1) parallel
- (2) horizontal
- (3) perpendicular
- (4) intersecting, but not perpendicular

**14. Which graph represents a circle whose equation is (x + 3)² + (y – 1)² = 4?**

- (1) 25
- (2) 30
- (3) 40
- (4) 46

**17. When the transformation T _{2,1 } 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)

**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

If CR = 24 and RF = 2x – 6, what is the value of x?

- (1) 9
- (2) 12
- (3) 15
- (4) 27

**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

**Geometry 26 January 2016 Questions Answers Keys**

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