# Geometry 29 January 2014

Geometry 29 January 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Wednesday, January 29, 2014 — 9:15 a.m. to 12:15 p.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

• (1) (1,3)
• (2) (2,8)
• (3) (5,1)
• (4) (14,0)

2. Which diagram shows the construction of a 45° angle?

3. What are the coordinates of the center and the length of the radius of the circle whose equation is (x + 1)² + (y – 5)² = 16?

• (1) (1,- 5) and 16
• (2) (- 1,5) and 16
• (3) (1,- 5) and 4
• (4) (- 1,5) and 4
Answer: (4) (- 1,5) and 4

4. If distinct planes R and S are both perpendicular to line ℓ, which statement must always be true?

• (1) Plane R is parallel to plane S.
• (2) Plane R is perpendicular to plane S.
• (3) Planes R and S and line ℓ are all parallel.
• (4) The intersection of planes R and S is perpendicular to line ℓ.
Answer: (1) Plane R is parallel to plane S.

5. If ΔABC and its image, ΔA’B’C’, are graphed on a set of axes, ΔABC ≅ ΔA’B’C’ under each transformation except

• (1) D2
• (2) R90°
• (3) ry = x
• (4) T(-2,3)

6. A right rectangular prism is shown in the diagram below.

Which pair of edges are not coplanar?

7. How many points in the coordinate plane are 3 units from the  origin and also equidistant from both the x-axis and the y-axis?

• (1) 1
• (2) 2
• (3) 8
• (4) 4

8. As shown below, the medians of ΔABC intersect at D.

• (1) 8
• (2) 9
• (3) 3
• (4) 4

9. The solution of the system of equations y = x² – 2 and y = x is

• (1) (1,1) and (- 2,- 2)
• (2) (2,2) and (- 1,- 1)
• (3) (1,1) and (2,2)
• (4) (- 2,- 2) and (- 1,- 1)
Answer: (2) (2,2) and (- 1,- 1)

10. Line ℓ passes through the point (5,3) and is parallel to line k whose equation is 5x + y = 6. An equation of line ℓ is

• (1) y =1/5x + 2
• (2) y = – 5x + 28
• (3) y = 1/5x – 2
• (4) y = – 5x – 28
Answer: (2) y = – 5x + 28

Which conclusion can be proven?

12. In the diagram below, four pairs of triangles are shown. Congruent corresponding parts are labeled in each pair.

Using only the information given in the diagrams, which pair of triangles can not be proven congruent?

• (1) A
• (2) B
• (3) C
• (4) D

If MN = 8, ML = 5, and NL = 6, the perimeter of trapezoid BMNC is

• (1) 35
• (2) 31
• (3) 28
• (4) 26

What is m∠ACR?

• (1) 125
• (2) 115
• (3) 65
• (4) 55

15. Which equation represents circle O shown in the graph below?

• (1) x² + (y – 2)² = 10
• (2) x² + (y + 2)² = 10
• (3) x² + (y – 2)2 = 25
• (4) x² + (y + 2)2 = 25
Answer: (4) x² + (y + 2)2 = 25

16. For which measures of the sides of ABC is angle B the largest angle of the triangle?

• (1) AB = 2, BC = 6, AC = 7
• (2) AB = 6, BC = 12, AC = 8
• (3) AB = 16, BC = 9, AC = 10
• (4) AB = 18, BC = 14, AC = 5
Answer: (1) AB = 2, BC = 6, AC = 7

17. What is the measure of the largest exterior angle that any regular polygon can have?

• (1) 60°
• (2) 90°
• (3) 120°
• (4) 360°

18. As shown in the diagram below, a landscaper uses a cylindrical lawn  roller on a lawn. The roller has a radius of 9 inches and a width of 42 inches.

To the nearest square inch, the area the roller covers in one complete rotation is

• (1) 2,374
• (2) 2,375
• (3) 10,682
• (4) 10,688

If m∠ACB = 38, what is m∠AOB?

• (1) 71
• (2) 104
• (3) 142
• (4) 161

20. What is the perimeter of a square whose diagonal is 3√2?

• (1) 18
• (2) 12
• (3) 9
• (4) 6