Represent transformations as functions on points and compare distance/angle-preserving transformations with non-rigid transformations.
Interpret transformation notation as a function on a point
Problem
Use the transformation \(T(x,y)=(x+3,y-2)\) to find the image of the point \((1,~5)\).
Big Picture
What this problem is really about
Transformation notation behaves like ordinary function notation: one ordered pair is the input, and one ordered pair is the output. We’ll match each input coordinate to its own expression, evaluate the two expressions independently, and keep their order fixed when assembling the image point.
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