Verify that dilations scale line segments by the dilation scale factor.
Find the image length of a segment after a dilation
Problem
The original segment has length \(14\). What is the image length after a dilation with scale factor \(2\)?
Big Picture
What this problem is really about
Segment length is a one-dimensional measure, so a dilation multiplies it by the absolute scale factor. We’ll source the original length and factor, apply the relationship in the forward direction, distinguish multiplication from adding or dividing, and confirm that the image-to-original ratio recovers the factor.
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