Problem preview

G-CO.2 Warmup M1-037-A12-V04

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

Correct an error in a transformed image point

Problem

A student claims that a \(90°\) counterclockwise rotation about the origin maps \((4,-1)\) to \((-4,1)\). Analyze the claim by stating the rule, identifying the error, finding the correct image, and verifying the result.

Source error: The student claims a 90° counterclockwise rotation sends (4,-1) to (-4,1), which instead negates both coordinates as in a 180° rotation.

Answer choices

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Preview only

rule = (x,y)→(-x,-y); error = none; correct image = (-4,1); check = (-4,1)

rule = (x,y)→(y,-x); error = wrong sign only; correct image = (-1,-4); check = (-1,-4)

rule = (x,y)→(y,x); error = negated x; correct image = (-1,4); check = (-1,4)

rule = (x,y)→(-y,x); error = changed both signs as for a 180° rotation instead of swapping coordinates and negating original y; correct image = (1,4); check = (-(-1),4)=(1,4)

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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: Correct an error in a transformed image point