Geometry 17 August 2017

Geometry 17 August 2017 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY
Thursday, August 17, 2017 — 12:30 to 3:30 p.m., only
Student Name:________________________________________________________
School Name: ________________________________________________________

1. A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three dimensional object?

  • (1) cone
  • (2) cylinder
  • (3) pyramid
  • (4) rectangular prism
Answer: (2) cylinder 

2. The image of DEF is DEF. Under which transformation will the triangles not be congruent?

  • (1) a reflection through the origin
  • (2) a reflection over the line y x
  • (3) a dilation with a scale factor of 1 centered at (2,3)
  • (4) a dilation with a scale factor of 3/2 centered at the origin
Answer: (4) a dilation with a scale factor of 3/2 centered at the origin 

3. The vertices of square RSTV have coordinates R(- 1,5), S(- 3,1), T(- 7,3), and V(- 5,7). What is the perimeter of RSTV?

  • (1) √20
  • (2) √40
  • (3) 4√20
  • (4) 4√40
Answer: (3) 4√20 
  • (1) 25
  • (2) 50
  • (3) 65
  • (4) 115
Answer: (1) 25  
  • (1) 2.70
  • (2) 3.34
  • (3) 5.28
  • (4) 8.25
Answer: (4) 8.25 

6. As shown in the graph below, the quadrilateral is a rectangle.

Which transformation would not map the rectangle onto itself?

  • (1) a reflection over the x-axis
  • (2) a reflection over the line x 4
  • (3) a rotation of 180° about the origin
  • (4) a rotation of 180° about the point (4,0)
Answer: (3) a rotation of 180° about the origin 
  • (1) 14.0
  • (2) 5.1
  • (3) 3.3
  • (4) 4.0
Answer: (4) 4.0 

8. In the diagram below of parallelogram ROCK, m∠C is 70° and  m∠ROS is 65°.

What is m∠KSO?

  • (1) 45°
  • (2) 110°
  • (3) 115°
  • (4) 135°
Answer: (4) 135° 

9. In the diagram below, ∠GRS ≅ ∠ART, GR = 36, SR = 45, AR = 15, and RT = 18.

Which triangle similarity statement is correct?

  • (1) ΔGRS ∼ ΔART by AA.
  • (2) ΔGRS ∼ ΔART by SAS.
  • (3) ΔGRS ∼ ΔART by SSS.
  • (4) ΔGRS is not similar to ΔART
Answer: (4) ΔGRS is not similar to ΔART 

10. The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

  • (1) 3x – 4y = 9
  • (2) 3x + 4y = 9
  • (3) 4x – 3y = 9
  • (4) 4x + 3y = 9
Answer: (4) ΔGRS is not similar to ΔART 
  • (1) 59°
  • (2) 62°
  • (3) 118°
  • (4) 121°
Answer: (4) 121° 
  • (1) 3√5
  • (2) 3√6
  • (3) 3
  • (4) 9
Answer: (2) 3√6 

13. A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously rotated around a straight line to form an object whose volume is 150π.

Which line could the rectangle be rotated around?

  • (1) a long side
  • (2) a short side
  • (3) the vertical line of symmetry
  • (4) the horizontal line of symmetry
Answer: (3) the vertical line of symmetry 

14. If ABCD is a parallelogram, which statement would prove that ABCD is a rhombus?

Answer: (3)  

15. To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram below.

What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree?

  • (1) 4.76
  • (2) 4.78
  • (3) 85.22
  • (4) 85.24
Answer: (1) 4.76 

What is the ratio of the area of ΔCFE to the area of ΔCAB?

  • (1) 1:1
  • (2) 1:2
  • (3) 1:3
  • (4) 1:4
Answer: (4) 1:4 
  • (1) (1,1)
  • (2) (7,3)
  • (3) (9.6,3.6)
  • (4) (6.4,2.8)
Answer: (1) (1,1)  

Which lengths would make triangle KLM a right triangle?

  • (1) LM = 13 and KN = 6
  • (2) LM = 12 and NM = 9
  • (3) KL = 11 and KN = 7
  • (4) LN = 8 and NM = 10
Answer: (2) LM = 12 and NM = 9  
  • (1) 3.3
  • (2) 3.9
  • (3) 5.3
  • (4) 11.7
Answer: (1) 3.3  

20. The 2010 U.S. Census populations and population densities are shown in the table below.

Based on the table above, which list has the states’ areas, in square miles, in order from largest to smallest?

  • (1) Illinois, Florida, New York, Pennsylvania
  • (2) New York, Florida, Illinois, Pennsylvania
  • (3) New York, Florida, Pennsylvania, Illinois
  • (4) Pennsylvania, New York, Florida, Illinois
Answer: (1) Illinois, Florida, New York, Pennsylvania 

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