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G-GPE.4 Warmup M2-043-A03-V01

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

Compare two coordinate slopes for perpendicularity

Problem

Use slopes to classify the supporting lines of \(AB\):\(A(0,0)\),\(B(2,3)\); \(CD\):\(C(1,1)\),\(D(4,-1)\).

Neutral coordinate reference listing A (0, 0), B (2, 3), C (1, 1), and D (4, negative 1), without supporting lines, an angle marker, or a classification. Open full size
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What this problem is really about

Different slopes are not automatically perpendicular; their directions must satisfy a right-angle criterion. We’ll compute each rise-over-run consistently, check first for the horizontal-vertical special case, multiply finite nonzero slopes to test for negative reciprocals, and connect that algebraic result to the supporting lines’ angle.

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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
Compare two coordinate slopes for perpendicularity