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?

Question

Answer in 3-4 sentences.

Answer 1

The dilation of line AB with a scale factor of 3 and a center of dilation at the origin will cause line A'B' to be three times longer than line AB. The relative location of line A'B' will remain the same as line AB since the center of dilation is at the origin. If line AB was dilated with a scale factor of 1/3, line A'B' would be one-third the length of line AB, resulting in a smaller size compared to line AB. The relative location of line A'B' would still remain the same.