GOZUNTA
Try it now
Problem preview
G-GPE.4 Warmup M1-044-A01-V01

Use coordinates, distance, and algebra to prove or disprove simple geometric statements.

Use the distance formula to prove segments congruent

Problem

Use the distance formula to calculate the lengths of segments \(A(0,0)B(3,4)\) and \(C(1,1)D(4,5)\), then state the congruence conclusion.

Source coordinate plane: Segment AB runs from A(0,0) to B(3,4), and segment CD runs from C(1,1) to D(4,5); no lengths or congruence conclusion are shown. Open full size
Big Picture

What this problem is really about

A coordinate congruence proof is really a comparison of displacement, not a visual judgment about the segments. Compute each horizontal and vertical change with a consistent endpoint order, compare the sums of their squares, and take square roots only if the problem requires the actual lengths; equal lengths then justify segment congruence.

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 I
Standard
G-GPE.4
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Problem type
Use the distance formula to prove segments congruent