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M1-044-A13-V02
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G-GPE.4
Warmup
M1-044-A13-V02
Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Disprove a geometric claim with coordinate evidence
Problem
Test the claim that the ordered vertices \(P(0,0)\), \(Q(4,0)\), \(R(4,2)\), \(S(0,3)\) form a rectangle. Give the relevant coordinate measurements, assess the required condition, and state the conclusion.
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A
claim = false; measurements = PS and QR are both vertical, but mPQ=0 and mRS=-1/4; violated condition = opposite sides PQ and RS are not parallel; conclusion = PQRS is not a parallelogram and therefore not a rectangle
B
claim = true; measurements = PS and QR vertical, mPQ=0, mRS=-1/4; condition assessment = one right angle establishes a rectangle; conclusion = PQRS is a rectangle
C
claim = true; measurements = mPQ=0 and mRS=-1/4; condition assessment = both slopes are defined and therefore parallel; conclusion = PQRS is a rectangle
D
claim = true; measurements = PS and QR vertical, mPQ=0, mRS=0; condition assessment = both opposite pairs are parallel; conclusion = PQRS is a rectangle
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Curriculum context
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 Disprove a geometric claim with coordinate evidence
