GOZUNTA
Try it now
Problem preview
G-SRT.1.a Warmup M2-045-A07-V01

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 \(y=1\),target \(y=3\),center \(O=(0,0)\).

Unworked feasibility setup with center O(0,0), source line y=1 through P(−2,1) and Q(2,1), and target line y=3 shown dashed; a positive dilation is required, but k and feasibility are not supplied. Open full size
Big Picture

What this problem is really about

Parallel appearance is necessary for non-center image lines, but feasibility also requires one consistent positive scale. We’ll check whether the source contains the center, derive how its signed offset transforms, solve for the required factor from the target offset, and map representative points to confirm the complete target line.

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
Decide whether one line can be a dilation image of another