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G-SRT.1.a Warmup M2-045-A02-V03

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

Derive and verify a parallel image line under dilation

Problem

Verify the image-line parallelism for center\((0,0)\),\(k=3\),original \(y=2x+1\).

Unworked setup with center O(0,0), k=3, and source line y=2x+1 represented by P(−1,−1) and Q(1,3); the line does not contain O, and image points, image equation, and classification are not shown. 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
Derive and verify a parallel image line under dilation