Verify that dilations scale line segments by the dilation scale factor.
Find the image length of a segment after a dilation
Problem
Segment \(AB\) has length \(8~\text{units}\) and is dilated by \(\text{scale}~\text{factor}~3\). What is the image length \(A'B'\)?
Big Picture
What this problem is really about
A dilation scale factor is a multiplicative length ratio, regardless of the segment’s direction or the center’s location. We’ll identify the original length and positive factor, multiply them in the forward original-to-image direction, preserve the length units, and divide image by original as a quick ratio check.
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