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G-GPE.4 Warmup M2-043-A09-V02

Use coordinates to prove simple geometric theorems, including simple circle theorems.

Verify a diameter/right-angle claim with squared lengths

Problem

A circle has diameter endpoints \(P\)\((0,-4)\) and \(Q\)\((0,4)\), with center \(O\) at their midpoint. Does \(R\)\((3,0)\) lie on the circle and make \(\angle~PRQ\) a right angle? Use squared lengths to decide.

Neutral coordinate reference listing diameter endpoints P (0, negative 4), Q (0, 4), and test point R (3, 0), without a circle, triangle, or angle conclusion. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GPE.4
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Use coordinates to prove simple geometric theorems, including simple circle theorems.
Problem type
Verify a diameter/right-angle claim with squared lengths