Question

When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, every point on line AB is moved away from the origin, becoming three times farther from the origin while maintaining its direction. This results in a new line, A′B′, that is parallel to the original line AB and also does not pass through the origin. If the scale factor were increased to 13, the points on line AB would move even farther from the origin, becoming thirteen times their original distance while still remaining parallel. In both cases, the orientation of the line remains unchanged, but the distance from the origin increases with a larger scale factor.


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Answer 1

When line AB is enlarged by a scale factor of 3 with the center of dilation at the origin, every point on line AB moves away from the origin and becomes three times farther away while keeping the same direction. This creates a new line, A'B', that is parallel to the original line AB and does not go through the origin.

If we increase the scale factor to 13, the points on line AB will move even farther away, becoming thirteen times their original distance from the origin, while still remaining parallel. In both cases, the direction of the line stays the same, but the distance from the origin increases with a larger scale factor.