Question

Line AB is on the coordinate plane and does not pass through the origin. Line AB is dilated with a scale factor of 3 and a center of dilation at the origin to create line A'B'. Describe the effect of the dilation on line AB. In particular, make sure to describe the relative location and the size of line A'B' compared to line AB. If line AB was dilated with a scale factor of 1/3, how would your answer change?

short answer

Answer 1

When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, line A'B' will be three times longer than line AB. Line A'B' will also maintain the same direction as line AB.

If line AB was dilated with a scale factor of 1/3, the effect would be opposite. Line A'B' would be one-third of the length of line AB, making it shorter. The direction would still be the same as line AB.