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?(4 points)

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1 answer

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 effect is that line A'B' would be three times as long as line AB and would pass through the origin. The relative location of the two lines would change as line A'B' would be centered at the origin while line AB would not pass through the origin.

If line AB was dilated with a scale factor of 13, the effect would be that line A'B' would be thirteen times as long as line AB and would pass through the origin. The relative location and size of the two lines compared to each other would be more significant with a scale factor of 13 than with a scale factor of 3.