Below are the questions with answers and explanations for Part 2 of the New York State Geometry Regents (not Common Core) exam for January 2016. Part I questions appeared in here.
29. The sides of a triangle measure 7, 4, and 9. If the longest side of a similar triangle measures 36, determine and state the length of the shortest side of this triangle.
The triangles are similar so the sides are proportional. Write a proportion:
4 / 9 = x / 36
9x = (4)(36)
9x = 144
x = 16. The shortest side of the triangle is 16.
Or, you can state that 36/9 = 4. The Scale factor is 4. Therefore the shortest side is 4 * 4 = 16.
30. Triangle ABC has coordinates A(6, -4), B(0,2), and C(6,2). On the set of axes below, graph and label triangle A'B'C', the image of triangle ABC after a dilation of 1/2.
Graph the points A'(3, -2), B'(0, 1), C'(3, 1) and draw the lines. Don't forget to label the points.
31. In parallelogram RSTU, m<R = 5x - 2 and m<S = 3x + 10. Determine and state the value of x.
R and S are consecutive angles in a parallelogram, so they are supplementary.
Therefore, 5x - 2 + 3x + 10 = 180
8x + 8 = 180
8x = 172
x = 22
If you set them equal to each other, that would be a conceptual error. You would have lost one point for that. You could get one point if your answer is consistent with the error.
32. Determine and state the length of a line segment whose endpoints are (6,4) and (-9, -4).
Use the Distance Formula, or Pythagorean Theorem.
Sqrt ( (-9-6)2 + (-4-4)2) =
Sqrt ( (-15)2 + (-8)2) =
Sqrt ( 225 + 64 ) =
sqrt ( 289 ) = 17.
If you figured that the change in x was 15 and change in y was 8, you could have used Pythagroean Theorem to get 17, also.
33. The base of a right pentagonal prism has an area of 20 square inches. If the prism has an altitude of 8 inches, determine and state the volume of the prism, in cubic inches.
V = Area of Base * Height = 20 * 8 = 160.
That seems like the easiest two points you'll get. I reread it three times thinking I missed something.
34. Using a compass and a straightedge, construct the bisector of <CDE. [Leave all construction marks.]
Construction coming soon. They aren't easy to do on the computer.
Steps: 1. From D make an arc that intersects DE and DC.
2. From the point you made on ED, make an arc inside the pentagon.
3. From the point you made on DC, make another arc the same size as the last one so that they overlap.
4. With the straightedge, draw the angle bisector from point D to the point where the two arcs intersected.