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:________________________________________________________

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**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 ****x ^{2} + y^{2} – 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

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