Represent transformations as functions on points and compare distance/angle-preserving transformations with non-rigid transformations.
Infer a coordinate transformation rule from point pairs
Problem
Infer the unique transformation from this allowed family: translations; reflections across the \(x\text{-}\text{axis}\) or \(y\text{-}\text{axis}\); rotations of \(90°\), \(180°\), or \(270°\) counterclockwise about the origin. It maps \((1,2)\to~(5,1)\) and \((3,4)\to~(7,3)\). Give its name and coordinate rule, and verify both mappings.
Big Picture
What this problem is really about
One point pair can suggest a rule, but the second pair is what tests whether the pattern is truly consistent. We’ll compute image-minus-source coordinate changes for both mappings, compare those results with the allowed transformation families, and substitute back into every supplied pair before naming the function.
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