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

**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)

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 x ^{2} + y^{2} – 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

- (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.

**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

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

**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?**

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