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

**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

**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

- (1) 25
- (2) 50
- (3) 65
- (4) 115

- (1) 2.70
- (2) 3.34
- (3) 5.28
- (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)

- (1) 14.0
- (2) 5.1
- (3) 3.3
- (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°

**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

**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

- (1) 59°
- (2) 62°
- (3) 118°
- (4) 121°

- (1) 3√5
- (2) 3√6
- (3) 3
- (4) 9

**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

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

**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

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

- (1) (1,1)
- (2) (7,3)
- (3) (9.6,3.6)
- (4) (6.4,2.8)

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

- (1) 3.3
- (2) 3.9
- (3) 5.3
- (4) 11.7

**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

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