# Geometry 17 June 2016

Geometry 17 June 2016 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (Common Core)
Friday, June 17, 2016 — 1:15 to 4:15 p.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

1. A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three dimensional object below is generated by this rotation?

2. A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?

• (1) 9 inches
• (2) 2 inches
• (3) 15 inches
• (4) 18 inches

3. Kevin’s work for deriving the equation of a circle is shown below.

x² + 4x – (y² – 20)

STEP 1                 x² +4x = – y² + 20
STEP 2     x² + 4x + 4 = – y² + 20 – 4
STEP 3         (x + 2)² =  – y² + 20 – 4
STEP 4                   (x + 2)² = y² = 16

In which step did he make an error in his work?

• (1) Step 1
• (2) Step 2
• (3) Step 3
• (4) Step 4
• (1) a translation of two units down
• (2) a reflection over the x-axis
• (3) a reflection over the y-axis
• (4) a clockwise rotation of 90° about the origin
Answer: (1) a translation of two units down

5. Using the information given below, which set of triangles can not be  proven similar?

6. A company is creating an object from a wooden cube with an edge length of 8.5 cm. A right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood?

• (1) (8.5)³ – π(8)²(8)
• (2) (8.5)³ – π(4)²(8)
• (3) (8.5)³ – ¹⁄3π(8)²(8)
• (4) (8.5)³ – ¹⁄3π(4)²(8)

7. Two right triangles must be congruent if

• (1) an acute angle in each triangle is congruent
• (2) the lengths of the hypotenuses are equal
• (3) the corresponding legs are congruent
• (4) the areas are equal
Answer: (3) the corresponding legs are congruent

8. Which sequence of transformations will map ABC onto A’B’C’?

• (1) reflection and translation
• (2) rotation and reflection
• (3) translation and dilation
• (4) dilation and rotation

Which statement must always be true?

• (1) ∠BAC ≅ ∠BOC
• (2) m∠BAC = ½ m∠BOC
• (3) ΔBAC and ΔBOC are isosceles.
• (4) The area of ΔBAC is twice the area of ΔBOC.
Answer: (2) m∠BAC = ½ m∠BOC

11. A 20-foot support post leans against a wall, making a 70° angle with the ground. To the nearest tenth of a foot, how far up the wall will the support post reach?

• (1) 6.8
• (2) 6.9
• (3) 18.7
• (4) 18.8
• (1) y + 1 = 43 (x + 3)
• (2) y + 1 = – ¾ (x + 3)
• (3) y – 6 =  43(x – 8)
• (4) y – 6 = – ¾ (x – 8)
Answer: (1) y + 1 = 43 (x + 3)

If SU = h, UT = 12, and RT = 42, which value of h will make ΔRST a right triangle with ∠RST as a right angle?

• (1) 6√3
• (2) 6√10
• (3) 6√14
• (4) 6√35

14. In the diagram below, ΔABC has vertices A(4,5), B(2,1), and C(7,3).

15. In the diagram below, ΔERM ∼ ΔJTM.

Which statement is always true?

16. On the set of axes below, rectangle ABCD can be proven congruent to rectangle KLMN using which transformation?

• (1) rotation
• (2) translation
• (3) reflection over the x-axis
• (4) reflection over the y-axis
Answer: (3) reflection over the x-axis

• (1) 10
• (2) 12
• (3) 17
• (4) 22.5

18. Seawater contains approximately 1.2 ounces of salt per liter on average. How many gallons of seawater, to the nearest tenth of a gallon, would contain 1 pound of salt?

• (1) 3.3
• (2) 3.5
• (3) 4.7
• (4) 13.3

20. A hemispherical water tank has an inside diameter of 10 feet. If water has a density of 62.4 pounds per cubic foot, what is the weight of the water in a full tank, to the nearest pound?

• (1) 16,336
• (2) 32,673
• (3) 130,690
• (4) 261,381