# Geometry 02 June 2016

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
Answer: (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
Answer: (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
Answer: (1) y =  ½x + 6

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
Answer: (4) sin A = cos B

14. The equation of a circle is x2  y2  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