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 size of line A′B′
compared to line AB
. If Line AB
was dilated with a scale factor of 13
, how would your answer change?

Answer 1

The dilation with a scale factor of 3 and a center of dilation at the origin stretches line AB by a factor of 3. This means that line A'B' will be three times longer than line AB. The relative location of A'B' will remain the same as line AB since the center of dilation is at the origin, and the origin is a fixed point that does not move.

If line AB was dilated with a scale factor of 13, the effect would be similar but more extreme. Line AB would be stretched by a factor of 13, making line A'B' 13 times longer than line AB. The relative location of A'B' would still remain the same compared to line AB, as the center of dilation is still at the origin.