Problem preview
G-CO.2 Warmup M1-037-A05-V01

Represent transformations as functions on points and compare distance/angle-preserving transformations with non-rigid transformations.

Determine whether a transformation preserves distance

Problem

For translation \(T(x,y)=(x+5,y-2)\), determine whether every pairwise distance is preserved.

Big Picture

What this problem is really about

Distance preservation concerns the separation between two points, not how far either point travels during the transformation. We’ll apply the rule to a generic pair, subtract their image coordinates, and see what happens to the common movement before comparing the original and image segment lengths.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
G-CO.2
Category
Geometry
Domain
Congruence
Objective
Represent transformations as functions on points and compare distance/angle-preserving transformations with non-rigid transformations.
Problem type
Determine whether a transformation preserves distance