Problem preview

G-CO.2 Warmup M1-037-A05-V04

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

Determine whether a transformation preserves distance

Problem

For rotation \(R(x,y)=(-y,x)\), a \(90°\) counterclockwise rotation about the origin, determine whether every pairwise distance is preserved.

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distance preserved = no; segment-length scale factor = 90; class = non-rigid

distance preserved = yes; segment-length scale factor = -1; class = reflection

distance preserved = yes; segment-length scale factor = 1; class = rigid motion (rotation)

distance preserved = no; segment-length scale factor = varies with distance from origin; class = non-rigid

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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