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°
Answer: (1) 53° 

Answer: (2)  

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
Answer: (1) 68.6 

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
Answer: (2) rectangle 

Answer: (1)  

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
Answer: (3) 15 

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°
Answer: (3) 60° 

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
Answer: (4) hemisphere 
Answer: (1)  

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
Answer: (3) 25 
  • (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 
Answer: (4)  
Answer: (4)  

If m∠CBF = 42.5°, then m∠EBF is

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

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?

Answer: (1)  

Download Geometry 23 January 2018 Questions Answers Keys

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