Problem preview
G-SRT.1.a Warmup M2-045-A03-V01

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

Dilate a line that passes through the center

Problem

Line \(y=2x\) passes through the center \((0,0)\). After a dilation with scale factor \(3\), what is the image of the line?

Big Picture

What this problem is really about

A line through the dilation center is a special invariant case because every point moves along a ray already contained in that line. We’ll test center incidence, apply the center-passing-line theorem, map a general point by scaling both coordinates, and verify that every image still satisfies the source equation.

Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now
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
Dilate a line that passes through the center