Problem preview

G-CO.4 Warmup M1-039-A03-V04

Define rotations, reflections, and translations using geometric language: angles, circles, perpendicular/parallel lines, and segments.

Define a reflection across a line

Problem

Define reflection across \(x=-1\).

Answer choices

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rule = (x,y)→(x-1,y); check = midpoint is (x-1/2,y); fixed points = none

rule = (x,y)→(-2-x,y); check = midpoint of P and P′ is (-1,y) on x=-1 and PP′ is horizontal, hence perpendicular to x=-1; fixed points = all and only points with x=-1

rule = (x,y)→(x,-2-y); check = PP′ is vertical; fixed points = y=-1

rule = (x,y)→(-x,y); check = midpoint lies on x=0; fixed points = x=0

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Curriculum context

Course: Math I
Standard: G-CO.4
Category: Geometry
Domain: Congruence
Objective: Define rotations, reflections, and translations using geometric language: angles, circles, perpendicular/parallel lines, and segments.
Problem type: Define a reflection across a line