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?

1 answer

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 the length of line AB and will be located at the same relative position as line AB, meaning it will have the same slope and direction.

If line AB was dilated with a scale factor of 1/3, line A'B' would be one-third the length of line AB and would still be located at the same relative position as line AB. The scale factor of 1/3 indicates that all distances on line AB would be contracted to one-third of their original length when creating line A'B'.