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′?

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.