Geometry 19 June 2015

Geometry 19 June 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Friday, June 19, 2015 — 1:15 to 4:15 p.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

1. Quadrilateral ABCD undergoes a transformation, producing quadrilateral A’B’C’D’. For which transformation would the area of A’B’C’D’ not be equal to the area of ABCD?

(1) a rotation of 90° about the origin
(2) a reflection over the y-axis
(3) a dilation by a scale factor of 2
(4) a translation defined by (x,y) → (x + 4,y – 1)

Answer: (3) a dilation by a scale factor of 2

2. The diameter of a sphere is 12 inches. What is the volume of the sphere to the nearest cubic inch?

(1) 288
(2) 452
(3) 905
(4) 7,238

Answer: (3) 905

3. A right rectangular prism is shown in the diagram below.

Which line segments are coplanar?

Answer: (4)

4. What are the coordinates of the image of point A(2,- 7) under the translation (x,y) → (x – 3,y + 5)?

(1) (- 1,- 2)
(2) (- 1,2)
(3) (5,- 12)
(4) (5,12)

Answer: (1) (- 1,- 2)

(1) (6,10)
(2) (- 6,4)
(3) (- 8,- 4)
(4) (18,16)

Answer: (2) (- 6,4)

(1) 20
(2) 16
(3) 12
(4) 10

Answer: (3) 12

7. What is an equation of the line that passes through the point (2,4) and is perpendicular to the line whose equation is 3y = 6x + 3?

(1) y = – ½x + 5
(2) y = – ½x + 4
(3) y = 2x – 6
(4) y = 2x

Answer: (1) y = – ½x + 5

8. In all isosceles triangles, the exterior angle of a base angle must always be

(1) a right angle
(2) an acute angle
(3) an obtuse angle
(4) equal to the vertex angle

Answer: (3) an obtuse angle

9. If ΔW’X’Y is the image of ΔWXY after the transformation R_90°, which statement is false?

Answer: (2)

10. Which equation represents the circle shown in the graph below?

(1) (x – 2)² + y² = 9
(2) (x + 2)² + y² = 9
(3) (x – 2)² + y² = 3
(4) (x + 2)² + y² = 3

Answer: (1) (x – 2)² + y² = 9

11. In quadrilateral ABCD, each diagonal bisects opposite angles. If m∠DAB = 70, then ABCD must be a

(1) rectangle
(2) trapezoid
(3) rhombus
(4) square

Answer: (3) rhombus

12. Which diagram illustrates a correct construction of an altitude of ΔABC?

Answer: (2)

(1) 33
(2) 48
(3) 57
(4) 66

Answer: (2) 48

14. Point A lies on plane P. How many distinct lines passing through point A are perpendicular to plane P ?

(1) 1
(2) 2
(3) 0
(4) infinite

Answer: (1) 1

15. Students made four statements about a circle.

A: The coordinates of its center are (4,-3).
B: The coordinates of its center are (-4,3).
C: The length of its radius is 5√2.
D: The length of its radius is 25.

If the equation of the circle is (x + 4)² (y – 3)² = 50, which statements are correct?