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 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?
When line AB is dilated with a scale factor of 3 and a center of dilation at the origin to create line A'B', the effect is that line A'B' is three times as long as line AB and extends out from the origin in the same direction as line AB. This means that line A'B' is parallel to line AB but is located three times farther away from the origin than line AB.
If line AB was dilated with a scale factor of 1/3, the effect would be that line A'B' is one third the length of line AB and extends out from the origin in the same direction as line AB. Therefore, line A'B' would be parallel to line AB but located one third of the distance away from the origin compared to line AB.