# Geometry 19 June 2018

Geometry 19 June 2018 Questions Answer Keys

The University Of The State Of New York
Regents High School Examination
Geometry
Tuesday, June 19, 2018 — 9:15 a.m. to 12:15 p.m., only

Student Name:________________________________________________________

School Name: _________________________________________________________

1. After a counterclockwise rotation about point X, scalene triangle ABC maps onto ΔRST, as shown in the diagram below.

Which statement must be true?

• (1) ∠A ∠R
• (2) ∠A ∠S
• (3) CB ≅ TR
• (4) CA ≅ TS
Answer: (1) ∠A ∠R

Which statement is true?

• (1) m∠D 28°
• (2) m∠A 43°
• (3) m∠ACD 71°
• (4) m∠BCE 109°
Answer: (3) m∠ACD 71°

3. In the diagram below, line m is parallel to line n. Figure 2 is the image of Figure 1 after a reflection over line m. Figure 3 is the image of Figure 2 after a reflection over line n.

Which single transformation would carry Figure 1 onto Figure 3?

• (1) a dilation
• (2) a rotation
• (3) a reflection
• (4) a translation
Answer: (4) a translation
• (1) 3.2
• (2) 4.8
• (3) 16.2
• (4) 19.2
Answer: (3) 16.2

5. Given square RSTV, where RS 9 cm. If square RSTV is dilated by a scale factor of 3 about a given center, what is the perimeter, in centimeters, of the image of RSTV after the dilation?

• (1) 12
• (2) 27
• (3) 36
• (4) 108
Answer: (4) 108
• (1) 48°
• (2) 47°
• (3) 43°
• (4) 34°
Answer: (2) 47°

7. The greenhouse pictured below can be modeled as a rectangular prism with a half-cylinder on top. The rectangular prism is 20 feet wide, 12 feet high, and 45 feet long. The half-cylinder has a diameter of 20 feet.

To the nearest cubic foot, what is the volume of the greenhouse?

• (1) 17,869
• (2) 24,937
• (3) 39,074
• (4) 67,349
Answer: (1) 17,869

8. In a right triangle, the acute angles have the relationship sin (2x + 4) cos (46).

What is the value of x?

• (1) 20
• (2) 21
• (3) 24
• (4) 25
Answer: (1) 20

Which statement is always true?

• (1) ΔDEF ≅ ΔCBF
• (2) ΔBAG ≅ ΔBAE
• (3) ΔBAG ~ ΔAEB
• (4) ΔDEF ~ ΔAEB
Answer: (4) ΔDEF ~ ΔAEB

10. The base of a pyramid is a rectangle with a width of 4.6 cm and a length of 9 cm. What is the height, in centimeters, of the pyramid if its volume is 82.8 cm3?

• (1) 6
• (2) 2
• (3) 9
• (4) 18
Answer: (1) 6

Which statement is always true?

• (1) AC/BC = DE/AE
• (2) AB/AD = BC/DE
• (3) AC/CE = BC/DE
• (4) DE/BC = DB/AB
Answer: (2) AB/AD = BC/DE

12. What is an equation of the line that passes through the point (6,8) and is perpendicular to a line with equation y = 3/2x + 5?

• (1) y – 8 = 3/2 (x – 6)
• (2) y – 8 = – 2/3 (x – 6)
• (3) y + 8 = 3/2 (x + 6)
• (4) y + 8 = – 2/3 (x + 6)
Answer: (2) y – 8 = – 2/3 (x – 6)
Answer: (4)
• (1) (–3,0)
• (2) (–2,2)
• (3) (–1,4)
• (4) (2,4)
Answer: (2) (–2,2)

15. Triangle DAN is graphed on the set of axes below. The vertices of 15 Triangle ΔDAN is graphed on the set of axes below. The vertices of

What is the area of DAN?

• (1) 60
• (2) 120
• (3) 20√13
• (4) 40√13
Answer: (1) 60

16. Triangle ABC, with vertices at A(0,0), B(3,5), and C(0,5), is graphed on the set of axes shown below.

Answer: (3)
• (1) 108°
• (2) 65°
• (3) 44°
• (4) 14°
Answer: (3) 44°

Which statement must always be true?

• (1) 3(MC) = SC
• (2) MC = 1/(SM)
• (3) RM = 2MC
• (4) SM = KM
Answer: (1) 3(MC) = SC

19. The regular polygon below is rotated about its center.

Which angle of rotation will carry the figure onto itself?

• (1) 60°
• (2) 108°
• (3) 216°
• (4) 540°
Answer: (3) 216°

20. What is an equation of circle O shown in the graph below?

• (1) x2 + 10x + y2 + 4y = –13
• (2) x2 – 10x + y2 – 4y = –13
• (3) x2 + 10x + y2 + 4y = – 25
• (4) x2 – 10x + y2 – 4y = – 25
Answer: (2) x2 – 10x + y2 – 4y = –13

Geometry 19 June 2018 Questions Answers Keys

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