Question

A dilation with a scale factor of 3 creates a line A'B that is parallel to A B, 3 times as long, and whose points are 3 times further from the origin; increasing the scale factor to 13 would make the line 13 times longer and 13 times further from the origin while still remaining parallel to the original line. make it simpler

Answer 1

A dilation from the origin with scale factor 3 sends segment AB to A'B' that is parallel to AB, three times as long, and three times as far from the origin. With scale factor 13, the image would be parallel, 13 times as long, and 13 times as far.

More generally: a dilation by factor k makes everything k times longer and k times farther from the origin.