Problem preview
G-SRT.1.a Warmup M2-045-A08-V01

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

Find the image equation of a line under dilation from the origin

Problem

A line \(y=2\) is dilated by center \((0,0)\), \(k=3\). What is the equation of its image?

Big Picture

What this problem is really about

An origin-centered dilation scales the constant height of every point on a horizontal line while preserving its orientation. We’ll apply the coordinate rule, transform the shared source height, map two distinct points to determine the full image line, and compare slopes and offsets to verify the image relationship.

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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
Find the image equation of a line under dilation from the origin