Geometry 02 June 2015 Questions Answer Keys

**The University of the State of New York **The University Of The State Of New York

Regents High School Examination

Geometry

(Common Core)

Tuesday, June 2, 2015 — 1:15 to 4:15 p.m., only

**Student Name:________________________________________________________**

**School Name:________________________________________________________**

**2. The vertices of Δ JKL have coordinates J(5,1), K(– 2, – 3), and L(– 4,1). Under which **

**transformation is the image Δ**

*J’K’L*not congruent to*JKL*?- (1) a translation of two units to the right and two units down
- (2) a counterclockwise rotation of 180 degrees around the origin
- (3) a reflection over the x-axis
- (4) a dilation with a scale factor of 2 and centered at the origin

**3. The center of circle Q has coordinates (3,–2). If circle Q passes through R(7,1), what is the length of its diameter?**

- (1) 50
- (2) 25
- (3) 10
- (4) 5

**4. In the diagram below, congruent figures 1, 2, and 3 are drawn.**

Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

- (1) a reflection followed by a translation
- (2) a rotation followed by a translation
- (3) a translation followed by a reflection
- (4) a translation followed by a rotation

**5. As shown in the diagram below, the angle of elevation from a point on the ground to the top of the tree is 34°.**

If the point is 20 feet from the base of the tree, what is the height of the tree, to the nearest tenth of a foot?

- (1) 29.7
- (2) 16.6
- (3) 13.5
- (4) 11.2

**6. Which figure can have the same cross section as a sphere?**

**7. A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pound per cubic foot. What is the weight, in pounds, of the contents in the container?**

- (1) 1,632
- (2) 408
- (3) 102
- (4) 92

**10. Which regular polygon has a minimum rotation of 45° to carry the polygon onto itself?**

- (1) octagon
- (2) decagon
- (3) hexagon
- (4) pentagon

**12. In scalene triangle ABC shown in the diagram below, m∠C = 90°**

Which equation is always true?

- (1) sin A = sin B
- (2) cos A = cos B
- (3) cos A = sin C
- (4) sin A = cos B

**14. The equation of a circle is x ^{2} y^{2} 6y 7. What are the coordinates of the center and the length of the radius of the circle?**

- (1) center (0,3) and radius 4
- (2) center (0, 3) and radius 4
- (3) center (0,3) and radius 16
- (4) center (0, 3) and radius 16

**19. A gallon of paint will cover approximately 450 square feet. An artist wants to paint all the outside surfaces of a cube measuring 12 feet on each edge. What is the least number of gallons of paint he must buy to paint the cube?**

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

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