Problem preview

G-CO.2 Warmup M1-037-A04-V04

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

Write a coordinate rule for dilation centered at the origin

Problem

This item uses the extended signed-homothety convention \(k=-2\) about the origin (standard school dilations usually require \(k>0\)). Identify the coordinate rule, distance multiplier, size/location effect, and whether it is rigid.

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rule = (x,y)→(-x/2,-y/2); distance multiplier = 1/2; effect = reduction on the opposite ray; rigid = no

rule = (x,y)→(2x,2y); distance multiplier = 2; effect = enlargement on the same ray; rigid = no

rule = (x,y)→(-2x,-2y); distance multiplier = -2; effect = negative lengths; rigid = yes

rule = (x,y)→(-2x,-2y); distance multiplier = 2; effect = enlargement by 2 with each nonzero image on the opposite ray through the origin; rigid = no

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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: Write a coordinate rule for dilation centered at the origin