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

Which statement is true?

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

**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

- (1) 3.2
- (2) 4.8
- (3) 16.2
- (4) 19.2

**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

- (1) 48°
- (2) 47°
- (3) 43°
- (4) 34°

**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

**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

Which statement is always true?

- (1) ΔDEF ≅ ΔCBF
- (2) ΔBAG ≅ ΔBAE
- (3) ΔBAG ~ ΔAEB
- (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 cm ^{3}?**

- (1) 6
- (2) 2
- (3) 9
- (4) 18

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}

**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}/_{2}x + 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)

- (1) (–3,0)
- (2) (–2,2)
- (3) (–1,4)
- (4) (2,4)

**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

**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.**

- (1) 108°
- (2) 65°
- (3) 44°
- (4) 14°

Which statement must always be true?

- (1) 3(MC) = SC
- (2) MC =
^{1}/_{3 }(SM) - (3) RM = 2MC
- (4) SM = KM

**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°

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

- (1) x
^{2}+ 10x + y^{2}+ 4y = –13 - (2) x
^{2}– 10x + y^{2}– 4y = –13 - (3) x
^{2}+ 10x + y^{2}+ 4y = – 25 - (4) x
^{2}– 10x + y^{2}– 4y = – 25

**Geometry 19 June 2018 Questions Answers Keys**

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