# Geometry 23 January 2018

Geometry 23 January 2018 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY
Tuesday, January 23, 2018 — 9:15 a.m. to 12:15 p.m., only
Student Name:________________________________________________________
School Name: ________________________________________________________

1. In the diagram below, a sequence of rigid motions maps ABCD onto JKLM.

If m∠A = 82°, m∠B = 104°, and m∠L = 121°, the measure of ∠M is

• (1) 53°
• (2) 82°
• (3) 104°
• (4) 121°

3. The graph below shows two congruent triangles, ABC and ABC.

Which rigid motion would map ΔABC onto ΔA’B’C’?

• (1) a rotation of 90 degrees counterclockwise about the origin
• (2) a translation of three units to the left and three units up
• (3) a rotation of 180 degrees about the origin
• (4) a reflection over the line y = x
Answer: (4) a reflection over the line y = x

4. A man was parasailing above a lake at an angle of elevation of 32°  from a boat, as modeled in the diagram below

If 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man?

• (1) 68.6
• (2) 80.9
• (3) 109.8
• (4) 244.4

5. A right hexagonal prism is shown below. A two-dimensional cross section that is perpendicular to the base is taken from the prism.

Which figure describes the two-dimensional cross section?

• (1) triangle
• (2) rectangle
• (3) pentagon
• (4) hexagon

7. An ice cream waffle cone can be modeled by a right circular cone with a base diameter of 6.6 centimeters and a volume of 54.45π cubic centimeters. What is the number of centimeters in the height of the waffle cone?

• (1) 20
• (2) 5
• (3) 15
• (4) 17

8. The vertices of ΔPQR have coordinates P(2,3), Q(3,8), and R(7,3). Under which transformation of ΔPQR are distance and angle measure preserved?

• (1) (x,y) → (2x, 3y)
• (2) (x,y) → (x + 2, 3y)
• (3) (x,y) → (2x, y + 3)
• (4) (x,y) → (x + 2, y + 3)
Answer: (4) (x,y) → (x + 2, y + 3)

What is m∠BAC?

• (1) 20°
• (2) 40°
• (3) 60°
• (4) 80°

10. Circle O is centered at the origin. In the diagram below, a quarter of circle O is graphed.

Which three-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?

• (1) cone
• (2) sphere
• (3) cylinder
• (4) hemisphere

12. The equation of a circle is x2 + y2 – 6x + 2y = 6. What are the coordinates of the center and the length of the radius of the circle?

• (1) center (- 3,1) and radius 4
• (2) center (3,- 1) and radius 4
• (3) center (- 3,1) and radius 16
• (4) center (3,- 1) and radius 16
Answer: (2) center (3,- 1) and radius 4
• (1) 15
• (2) 24
• (3) 25
• (4) 30
• (1) The image of the line has the same slope as the pre-image but a different y-intercept.
• (2) The image of the line has the same y-intercept as the pre-image but a different slope.
• (3) The image of the line has the same slope and the same y-intercept as the pre-image.
• (4) The image of the line has a different slope and a different y-intercept from the pre-image.
Answer: (1) The image of the line has the same slope as the pre-image but a different y-intercept.

15. Which transformation would not carry a square onto itself?

• (1) a reflection over one of its diagonals
• (2) a 90° rotation clockwise about its center
• (3) a 180° rotation about one of its vertices
• (4) a reflection over the perpendicular bisector of one side
Answer: (3) a 180° rotation about one of its vertices

If m∠CBF = 42.5°, then m∠EBF is

• (1) 42.5°
• (2) 68.75°
• (3) 95°
• (4) 137.5°

19. A parallelogram must be a rhombus if its diagonals

• (1) are congruent
• (2) bisect each other
• (3) do not bisect its angles
• (4) are perpendicular to each other
Answer: (4) are perpendicular to each other

20. What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x – 6y =15?