Geometry 19 June 2013

Geometry 19 June 2013 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Wednesday, June 19, 2013 — 9:15 a.m. to 12:15 p.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

If trapezoid RSTV is not isosceles, which triangle is equal in area to ΔRSV?

  • (1) ΔRQV
  • (2) ΔRST
  • (3) ΔRVT
  • (4) ΔSV
Answer: (2) ΔRST  

2. In the diagram below, ΔXYV ≅ ΔTSV.

Which statement can not be proven?

Answer: (2)   

3. In a park, two straight paths intersect. The city wants to install lampposts that are both equidistant from each path and also 15 feet from the intersection of the paths. How many lampposts are needed?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 4
Answer: (4) 4  

4. What are the coordinates of A’, the image of point A( – 3,4), after a rotation of 180° about the origin?

  • (1) (4, – 3)
  • (2) ( – 4, – 3)
  • (3) (3,4)
  • (4) (3, – 4)
Answer: (4) (3, – 4)  

5. Based on the construction below, which conclusion is not always true?

  • (1) AB ⊥ CD
  • (2) AB = CD
  • (3) AE = EB
  • (4) CE = DE
Answer: (2) AB = CD

6. Which equation represents the circle whose center is ( – 5,3) and that passes through the point ( – 1,3)?

  • (1) (x + 1)² + (y – 3)² = 16
  • (2) (x – 1)² + (y + 3)² = 16
  • (3) (x + 5)² + (y – 3)² = 16
  • (4) (x – 5)² + (y + 3)² = 16
Answer: (3) (x + 5)² + (y – 3)² = 16

7. As shown in the diagram below, when right triangle DAB is reflected over the x-axis, its image is triangle DCB.

  • (1) Distance is preserved under reflection.
  • (2) Orientation is preserved under reflection.
  • (3) Points on the line of reflection remain invariant.
  • (4) Right angles remain congruent under reflection.
Answer: (1) Distance is preserved under reflection.

8. In ΔABC, m∠A = 3x + 1, m∠B = 4x – 17, and m∠C = 5x – 20. Which type of triangle is ΔABC?

  • (1) right
  • (2) scalene
  • (3) isosceles
  • (4) equilateral
Answer: (3) isosceles

9. What is the equation for circle O shown in the graph below?

  • (1) (x – 3)² + (y + 1)² = 6
  • (2) (x + 3)² + (y – 1)² = 6
  • (3) (x – 3)² + (y + 1)² = 9
  • (4) (x + 3)² + (y – 1)² = 9
Answer: (3) (x – 3)² + (y + 1)² = 9

10. Point A is on line m. How many distinct planes will be perpendicular to line m and pass through point A?

  • (1) one
  • (2) two
  • (3) zero
  • (4) infinite
Answer: (1) one
  • (1) 6
  • (2) 7
  • (3) 9
  • (4) 12
Answer: (3) 9  

12. What are the coordinates of the center of a circle if the endpoints of its diameter are A(8, – 4) and B( – 3,2)?

  • (1) (2.5,1)
  • (2) (2.5,1)
  • (3) (5.5,3)
  • (4) (5.5,3)
Answer: (2) (2.5,1)  

13. Which graph could be used to find the solution to the following system of equations?

y = (x + 3)² – 1
x + y = 2

Answer: (2)  

14. What is the converse of “If an angle measures 90 degrees, then it is a right angle”?

  • (1) If an angle is a right angle, then it measures 90 degrees.
  • (2) An angle is a right angle if it measures 90 degrees.
  • (3) If an angle is not a right angle, then it does not measure 90 degrees.
  • (4) If an angle does not measure 90 degrees, then it is not a right angle.
Answer: (1) If an angle is a right angle, then it measures 90 degrees.
Answer: (2)  

16. What is the equation of a line passing through the point (6,1) and parallel to the line whose equation is 3x = 2y + 4?

Answer: (3)  

17. The volume of a sphere is approximately 44.6022 cubic centimeters. What is the radius of the sphere, to the nearest tenth of a centimeter?

  • (1) 2.2
  • (2) 3.3
  • (3) 4.4
  • (4) 4.7
Answer: (1) 2.2 
Answer: (4)  

19. Which set of equations represents two circles that have the same center?

  • (1) x² + (y + 4)² = 16 and (x + 4)² + y² = 16
  • (2) (x + 3)² + (y – 3)² = 16 and (x – 3)² + (y + 3)² = 25
  • (3) (x – 7)² + (y – 2)² = 16 and (x + 7)² + (y + 2)² = 25
  • (4) (x – 2)² + (y – 5)² = 16 and (x – 2)² + (y – 5)² = 25
Answer: (4) (x – 2)² + (y – 5)² = 16 and (x – 2)² + (y – 5)² = 25  
  • (1) ∠2 ≅ ∠4
  • (2) ∠7 ≅ ∠8
  • (3) ∠3 and ∠6 are supplementary
  • (4) ∠1 and ∠5 are supplementary
Answer: (3) ∠3 and ∠6 are supplementary

 

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