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G-SRT.1.a Warmup M2-045-A07-V04

Verify that dilations send non-center-passing lines to parallel lines and leave center-passing lines unchanged.

Decide whether one line can be a dilation image of another

Problem

Decide whether the target line can be the image of the source under a positive dilation with source \(x+y=0\),target \(x+y=6\),center \(O=(0,0)\).

Unworked feasibility setup with center O(0,0), source line x+y=0 through P(−2,2) and Q(2,−2), and target line x+y=6 shown dashed; a positive dilation is required, but feasibility is not supplied. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-SRT.1.a
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Verify that dilations send non-center-passing lines to parallel lines and leave center-passing lines unchanged.
Problem type
Decide whether one line can be a dilation image of another