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?
The dilation with a scale factor of 3 and a center of dilation at the origin will stretch line AB by a factor of 3. This means that the length of line A'B' will be 3 times the length of line AB. Additionally, line A'B' will be parallel to line AB and will pass through the origin.
If line AB was dilated with a scale factor of 1/3, the effect would be the opposite. Line A'B' would be compressed, so its length would be 1/3 times the length of line AB. It would still be parallel to line AB and pass through the origin.
can you make it more simple?
Certainly!
When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, line A'B' becomes three times longer than line AB. It remains parallel to line AB and passes through the origin.
If line AB is dilated with a scale factor of 1/3, line A'B' becomes one-third the length of line AB. It still remains parallel to line AB and passes through the origin.