Geometry 16 June 2017 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)

Friday, June 16, 2017 — 9:15 a.m. to 12:15 p.m., only

Student Name:________________________________________________________

School Name:________________________________________________________

**1. In the diagram below, ABC ≅ DEF.**

Which sequence of transformations maps ABC onto DEF?

- (1) a reflection over the x-axis followed by a translation
- (2) a reflection over the y-axis followed by a translation
- (3) a rotation of 180° about the origin followed by a translation
- (4) a counterclockwise rotation of 90° about the origin followed by a translation

**2. On the set of axes below, the vertices of PQR have coordinates P(6,7), Q(2,1), and R(1,3).**

What is the area of PQR?

- (1) 10
- (2) 20
- (3) 25
- (4) 50

**3. In right triangle ABC, m∠C 90°. If cos B = 5/13, which function also equals 5/13?**

- (1) tan A
- (2) tan
- (3) sin A
- (4) sin B

**4. In the diagram below, mABC 268°.**

What is the number of degrees in the measure of ∠ABC?

- (1) 134°
- (2) 92°
- (3) 68°
- (4) 46°

**5. Given ΔMRO shown below, with trapezoid PTRO, MR = 9,**

**MP = 2, and PO = 4.**

What is the length of TR?

- (1) 4.5
- (2) 5
- (3) 3
- (4) 6

**6. A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?**

- (1) The line segments are perpendicular, and the image is one-half of the length of the given line segment.
- (2) The line segments are perpendicular, and the image is twice the length of the given line segment.
- (3) The line segments are parallel, and the image is twice the length of the given line segment.
- (4) The line segments are parallel, and the image is one-half of the length of the given line segment.

**7. Which figure always has exactly four lines of reflection that map the figure onto itself?**

- (1) square
- (2) rectangle
- (3) regular octagon
- (4) equilateral triangle

__ __

**8. In the diagram below of circle O, chord DF bisects chord BC at E.**

If BC = 12 and FE is 5 more than DE, then FE is

- (1) 13
- (2) 9
- (3) 6
- (4) 4

**11. Which set of statements would describe a parallelogram that can always be classified as a rhombus?**

I. Diagonals are perpendicular bisectors of each other.

II. Diagonals bisect the angles from which they are drawn.

III. Diagonals form four congruent isosceles right triangles.

- (1) I and II
- (2) I and III
- (3) II and III
- (4) I, II, and III

**12. The equation of a circle is x ^{2} + y^{2} – 12y + 20 = 0. What are the coordinates of the center and the length of the radius of the circle?**

- (1) center (0,6) and radius 4
- (2) center (0, –6) and radius 4
- (3) center (0,6) and radius 16
- (4) center (0, –6) and radius 16

**16 . The pyramid shown below has a square base, a height of 7, and a volume of 84.**

What is the length of the side of the base?

- (1) 6
- (2) 12
- (3) 18
- (4) 36

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