Represent transformations as functions on points and compare distance/angle-preserving transformations with non-rigid transformations.
Write a coordinate rule for dilation centered at the origin
Problem
For a dilation centered at the origin with scale factor \(k=2\), identify the coordinate rule, distance multiplier, size effect, and whether the transformation is rigid.
A dilation scales the whole position vector from its center, so both coordinates must respond to the same factor. We’ll separate the signed coordinate rule from the nonnegative distance multiplier, then use that multiplier to classify the size change and test whether the transformation preserves lengths.
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