Worksheet for practicing geometric dilations on coordinate planes with scale factors and centers of dilation.

1. For problem 6:
- The original coordinates of triangle XYZ are:
- X: (-4, 2)
- Y: (6, 0)
- Z: (-2, -3)
- The scale factor is 1.5 and the center of dilation is (0, 0).
- To find the dilated coordinates, multiply each coordinate by the scale factor:
- X': (-4 * 1.5, 2 * 1.5) = (-6, 3)
- Y': (6 * 1.5, 0 * 1.5) = (9, 0)
- Z': (-2 * 1.5, -3 * 1.5) = (-3, -4.5)

2. For problem 7:
- The original coordinates of quadrilateral MNOP are:
- M: (2, 6)
- N: (6, 0)
- O: (2, -4)
- P: (-4, 0)
- The scale factor is 1/3 and the center of dilation is the origin (0, 0).
- To find the dilated coordinates, multiply each coordinate by the scale factor:
- M': (2 * 1/3, 6 * 1/3) = (2/3, 2)
- N': (6 * 1/3, 0 * 1/3) = (2, 0)
- O': (2 * 1/3, -4 * 1/3) = (2/3, -4/3)
- P': (-4 * 1/3, 0 * 1/3) = (-4/3, 0)

3. For problem 8:
- The original coordinates of quadrilateral MNOP are:
- M: (4, 3)
- N: (8, 0)
- O: (0, -4)
- P: (-4, 0)
- The dilated coordinates are:
- M': (2, 1.5)
- N': (4, 0)
- O': (0, -2)
- P': (-2, 0)
- The scale factor is found by comparing the original and dilated coordinates:
- For M: 2/4 = 0.5, 1.5/3 = 0.5
- For N: 4/8 = 0.5, 0/0 = 0 (but the x-coordinate is halved)
- For O: 0/0 = 0, -2/-4 = 0.5
- For P: -2/-4 = 0.5, 0/0 = 0
- The scale factor is 0.5 (or 1/2).
- The dilation of quadrilateral MNOP using the origin as the center is a reduction by a scale factor of 1/2.