Question

The coordinates of trapezoid ABCD are A(−4, 3), B(2, 3), C(4, −1) and D(−4, −1). A line segment runs through the trapezoid with endpoints Y(−4, 1) and Z(3, 1). If trapezoid ABCD is dilated by a scale factor of 3 creating the new trapezoid of A′B′C′D′, what can you say about the length of line segment Y′Z′?

Answer 1

We can say about the length of line segment Y'Z' will increase by the length of 3

Answer 2

The distance from point Y to the y-axis is 4 units and the distance from point Z to the y-axis is 3 units, then the lelgth of the segment YZ is 4+3=7 units.
If a scale factor is 3, then the length of Y'Z' will be 7·3=21 units.

P.S. In the added picture you can see trapezoid ABCD that was dilated by a scale factor 3 about the origin. This may help to understand that all linear values after dilation become multiplied by scale factor.