Final answer:
The slopes of a polygon's sides remain the same after a dilation, but the lengths are scaled by the dilation factor. To match the slopes and lengths of the sides after a dilation by the factor of 1.2, simply multiply each original length by 1.2 and pair with the original slope.
Step-by-step explanation:
The student's question deals with dilations in geometry, specifically how the lengths and slopes of a polygon's sides are affected by a dilation. We are given a polygon ABCD with sides of certain lengths and slopes, and we're asked to match these with the new lengths and slopes after a dilation by a scale factor of 1.2 from point A to form polygon A'B'C'D'. Since the slopes of lines are unaffected by dilations, they remain the same. However, the lengths of the sides are scaled by the factor of 1.2.
For each side, we multiply its original length by 1.2 to find the new length. For example, a side of 5 units will now be 5 units × 1.2 = 6 units. When you match the sides with the correct lengths and the unchanged slopes, we get the pairs:
- Slope of 0.25 with length of 5 units (unchanged slope, original length is about 4.17 units)
- Slope of 5 with length of 6 units (unchanged slope, original length is 5 units)
- Slope of -2 with length of 5.4 units (unchanged slope, original length is 4.5 units)
- Slope of 0 with length of 8.4 units (unchanged slope, original length is 7 units)