# Geometry 26 January 2017

Geometry 26 January 2017 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (Common Core)
Thursday, January 26, 2017 — 9:15 a.m. to 12:15 p.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

1. Which equation represents the line that passes through the point (2,2) and is parallel to y = ½x + 8?

• (1) y= ½ x
• (2) y = -2x – 3
• (3) y = ½x + 3
• (4) y = – 2x + 3
Answer: (3) y = ½x + 3

Which statement must be true?

• (1) m∠BAC = m∠AED
• (3) m∠DAE = ½m∠BAC
• (4) m∠ACB = ½m∠DAB

3. Given ΔABC ≅ ΔDEF, which statement is not always true?

• (1)
• (2) m∠A = m∠D
• (3) area of ΔABC = area of ΔDEF
• (4) perimeter of ΔABC = perimeter of ΔDEF

• (1) AB + BC + AC
• (2) ½AB + ½AC
• (3) 2AB + 2AC
• (4) AB + AC
• (1) square
• (2) rhombus
• (3) rectangle
• (4) parallelogram

6. Under which transformation would ΔA’B’C’, the image of ΔABC, not be congruent to ΔABC?

• (1) reflection over the y-axis
• (2) rotation of 90º clockwise about the origin
• (3) translation of 3 units right and 2 units down
• (4) dilation with a scale factor of 2 centered at the origin
Answer: (4) dilation with a scale factor of 2 centered at the origin

7. The diagram below shows two similar triangles.

• (1) 1.2
• (2) 5.6
• (3) 7.6
• (4) 8.8

8. A farmer has 64 feet of fence to enclose a rectangular vegetable garden. Which dimensions would result in the biggest area for this garden?

• (1) the length and the width are equal
• (2) the length is 2 more than the width
• (3) the length is 4 more than the width
• (4) the length is 6 more than the width
Answer: (1) the length and the width are equal

What is the perimeter of rectangle ABCD, to the nearest tenth?

• (1) 28.4
• (2) 32.8
• (3) 48.0
• (4) 62.4

10. Identify which sequence of transformations could map pentagon ABCDE onto pentagon A”B”C”D”E”, as shown below.

• (1) dilation followed by a rotation
• (2) translation followed by a rotation
• (3) line reflection followed by a translation
• (4) line reflection followed by a line reflection
Answer: (3) line reflection followed by a translation

11. A solid metal prism has a rectangular base with sides of 4 inches and 6 inches, and a height of 4 inches. A hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.

What is the approximate volume of the remaining solid, in cubic inches?

• (1) 19
• (2) 77
• (3) 93
• (4) 96

12. Given the right triangle in the diagram below, what is the value of x, to the nearest foot?

• (1) 11
• (2) 17
• (3) 18
• (4) 22
• (1) B'(5,2) and C'(1,- 2)
• (2) B'(6,1) and C'(0,- 1)
• (3) B'(5,0) and C'(1,- 2)
• (4) B'(5,2) and C'(3,0)
Answer: (1) B'(5,2) and C'(1,- 2)
• (1) 6
• (2) 22
• (3) 36
• (4) 48

16. A parallelogram is always a rectangle if

• (1) the diagonals are congruent
• (2) the diagonals bisect each other
• (3) the diagonals intersect at right angles
• (4) the opposite angles are congruent
Answer: (1) the diagonals are congruent

17. Which rotation about its center will carry a regular decagon onto itself?

• (1) 54°
• (2) 162°
• (3) 198°
• (4) 252°

18. The equation of a circle is x² + y² – 6y +1 = 0. What are the coordinates of the center and the length of the radius of this circle?

• (1) center (0,3) and radius  = 2√2
• (2) center (0,3) and radius = 2√2
• (3) center (0,6) and radius = √35
• (4) center (0,6) and radius = √35

19. Parallelogram ABCD has coordinates A(0,7) and C(2,1). Which statement would prove that ABCD is a rhombus?

• (1) (5,1)
• (2) (5,0)
• (3) (6,- 1)
• (4) (6,0)