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 effects of the dilation on Line AB . If line AB was dilated with a scale factor of 13 , 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 effects of the dilation are as follows:
1. Each point on line AB is multiplied by 3 in both the x and y directions.
2. Line A'B' is parallel to line AB.
3. Line A'B' is three times the distance from the origin as line AB.
If line AB was dilated with a scale factor of 13, the effects would be similar, but more dramatic:
1. Each point on line AB is multiplied by 13 in both the x and y directions.
2. Line A'B' is parallel to line AB.
3. Line A'B' is thirteen times the distance from the origin as line AB.
In both cases, the dilation causes line AB to stretch or shrink by the specified scale factor and move further away from the origin.