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

**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.

**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) D
_{2} - (2) R
_{90°} - (3) r
_{y = 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)

**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}/_{5}x + 2 - (2) y = – 5x + 28
- (3) y =
^{1}/_{5}x – 2 - (4) 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

**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

**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

**Geometry 29 January 2014 Questions Answers Keys**

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