# Geometry 12 August 2015

Geometry 12 August 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (Common Core)
Wednesday, August 12, 2015 — 8:30 to 11:30 a.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

1. A parallelogram must be a rectangle when its

• (1) diagonals are perpendicular
• (2) diagonals are congruent
• (3) opposite sides are parallel
• (4) opposite sides are congruent

2. If ΔA’B’C’ is the image of ΔABC, under which transformation will the triangles not be congruent?

• (1) reflection over the x-axis
• (2) translation to the left 5 and down 4
• (3) dilation centered at the origin with scale factor 2
• (4) rotation of 270° counterclockwise about the origin
Answer: (3) dilation centered at the origin with scale factor 2

3. If the rectangle below is continuously rotated about side w, which solid figure is formed?

• (1) pyramid
• (2) rectangular prism
• (3) cone
• (4) cylinder

4. Which expression is always equivalent to sin x when 0°< x <90°?

• (1) cos (90° – x)
• (2) cos (45° – x)
• (3) cos (2x)
• (4) cos x
Answer: (1) cos (90° – x)

5. In the diagram below, a square is graphed in the coordinate plane.

A reflection over which line does not carry the square onto itself?

• (1) x = 5
• (2) y = 2
• (3) y = x
• (4) x + y = 4

6. The image of ΔABC after a dilation of scale factor k centered at point A is ΔADE, as shown in the diagram below.

Which statement is always true?

7. A sequence of transformations maps rectangle ABCD onto rectangle A”B”C”D”, as shown in the diagram below

Which sequence of transformations maps ABCD onto ABCD and then maps ABCD onto A’B’C’D’?

• (1) a reflection followed by a rotation
• (2) a reflection followed by a translation
• (3) a translation followed by a rotation
• (4) a translation followed by a reflection
Answer: (1) a reflection followed by a rotation

If m∠R = 124°, what is m∠AFD?

• (1) 124°
• (2) 112°
• (3) 68°
• (4) 56°

9. If x² + 4x + y² – 6y – 12 = 0 is the equation of a circle, the length of the radius is

• (1) 25
• (2) 16
• (3) 5
• (4) 4
• (1) y = –23x + 5
• (2) y = – 23x – 3
• (3) y = 3 ⁄2x + 7
• (4) y = 3 ⁄2x – 8
Answer: (1) y = –23x + 5

11. Linda is designing a circular piece of stained glass with a diameter of 7 inches. She is going to sketch a square inside the circular region.

To the nearest tenth of an inch, the largest possible length of a side of the square is

• (1) 3.5
• (2) 4.9
• (3) 5.0
• (4) 6.9
• (1) 6.4
• (2) 8
• (3) 12.5
• (4) 16

13. In the diagram below, which single transformation was used to map triangle A onto triangle B?

• (1) line reflection
• (2) rotation
• (3) dilation
• (4) translation

14. In the diagram below, ΔDEF is the image of ΔABC after a clockwise  rotation of 180º and a dilation where AB = 3, BC = 5.5, AC = 4.5, DE = 6, FD = 9, and EF = 11.

Which relationship must always be true?

15. In the diagram below, quadrilateral ABCD is inscribed in circle P.

• (1) 70º
• (2) 72º
• (3) 108º
• (4) 110º

16. A hemispherical tank is filled with water and has a diameter of 10 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

• (1) 16,336
• (2) 32,673
• (3) 130,690
• (4) 261,381

17. In the diagram below, ΔABC ∼ΔADE.

Which measurements are justified by this similarity?

• (1) AD = 3, AB = 6, AE = 4, and AC = 12
• (2) AD = 5, AB = 8, AE = 7, and AC = 10
• (3) AD = 3, AB = 9, AE = 5, and AC = 10
• (4) AD = 2, AB = 6, AE = 5, and AC = 15
Answer: (4) AD = 2, AB = 6, AE = 5, and AC = 15

What is the area of the sector formed by angle FOH?

• (1) 2π
• (2) 3 ⁄2π
• (3) 6π
• (4) 24π

Given ΔAEC ∼ ΔBED, which equation is true?

20. A triangle is dilated by a scale factor of 3 with the center of dilation at the origin. Which statement is true?

• (1) The area of the image is nine times the area of the original triangle.
• (2) The perimeter of the image is nine times the perimeter of the original triangle.
• (3) The slope of any side of the image is three times the slope of the corresponding side of the original triangle.
• (4) The measure of each angle in the image is three times the measure of the corresponding angle of the original triangle.
Answer: (1) The area of the image is nine times the area of the original triangle.

Geometry 12 August 2015 Questions Answers Keys

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