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G-GPE.4 Warmup M1-044-A08-V01

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

Use coordinates to prove or disprove a right triangle

Problem

Use coordinates to decide whether points \(A(0,~0)\), \(B(3,~0)\), and \(C(0,~4)\) form a right triangle.

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What this problem is really about

A right-triangle check needs one perpendicular pair of sides that meet at the same vertex. Scan the coordinate changes for an immediate horizontal-versus-vertical pair; if that shortcut is unavailable, compare slopes or use the three squared side lengths with the converse of the Pythagorean theorem.

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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 coordinates to prove or disprove a right triangle