# Geometry 17 August 2016

Geometry 17 August 2016 Questions Answer Keys

The University of the State of New York
The University Of The State Of New York
Regents High School Examination
Geometry
(Common Core)

Student Name:________________________________________________________

School Name:________________________________________________________

1. In the diagram below, lines ℓ, m, n, and p intersect line r

Which statement is true?

• (1) ℓ || n
• (2) ℓ || p
• (3) m || p
• (4) m || n

2. Which transformation would not always produce an image that would be congruent to the original figure?

• (1) translation
• (2) dilation
• (3) rotation
• (4) reflection

3. If an equilateral triangle is continuously rotated around one of its medians, which 3-dimensional object is generated?

• (1) cone
• (2) pyramid
• (3) prism
• (4) sphere

4. In the diagram below, m∠BDC = 100°, m∠A = 50°, and m∠DBC = 30°.

Which statement is true?

• (1) Δ ABD is obtuse.
• (2) Δ ABC is isosceles.
• (3) m∠ABD 80°
• (4) Δ ABD is scalene.

5. Which point shown in the graph below is the image of point P after a counterclockwise rotation of 90° about the origin?

• (1) A
• (2) B
• (3) C
• (4) D

8. An equilateral triangle has sides of length 20. To the nearest tenth, what is the height of the equilateral triangle?

• (1) 10.0
• (2) 11.5
• (3) 17.3
• (4) 23.1
• (1) a rotation of 180 degrees about point E followed by a horizontal translation
• (2) a counterclockwise rotation of 90 degrees about point E followed by a horizontal translation
• (3) a rotation of 180 degrees about point E followed by a dilation with a scale factor of 2 centered at point E
• (4) a counterclockwise rotation of 90 degrees about point E followed by a dilation with a scale factor of 2 centered at point E

13. The cross section of a regular pyramid contains the altitude of the pyramid. The shape of this cross section is a

• (1) circle
• (2) square
• (3) triangle
• (4) rectangle

15. The coordinates of vertices A and B of Δ ABC are A(3,4) and B(3,12). If the area of Δ ABC is 24 square units, what could be the coordinates of point C?

• (1) (3,6)
• (2) (8, –3)
• (3) (3,8)
• (4) (6, –3)

16. What are the coordinates of the center and the length of the radius of the circle represented by the equation  x2 + y2 – 4x + 8y + 11 = 0?

• (1) center (2, 4) and radius 3
• (2) center (2,4) and radius 3
• (3) center (2, 4) and radius 9
• (4) center (2,4) and radius 9

17. The density of the American white oak tree is 752 kilograms per cubic meter. If the trunk of an American white oak tree has a circumference of 4.5 meters and the height of the trunk is 8 meters, what is the approximate number of kilograms of the trunk?

• (1) 13
• (2) 9694
• (3) 13,536
• (4) 30,456

18. Point P is on the directed line segment from point X(–6, –2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?

20. Tennis balls are sold in cylindrical cans with the balls stacked one on top of the other. A tennis ball has a diameter of 6.7 cm. To the nearest cubic centimeter, what is the minimum volume of the can that holds a stack of 4 tennis balls?

• (1) 236
• (2) 282
• (3) 564
• (4) 945