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G-GPE.4 Warmup M2-043-A02-V01

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

Compare two coordinate slopes for parallelism

Problem

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

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

Matching slopes establish matching directions, but they do not distinguish parallel lines from one coincident line. We’ll compute both slopes in consistent coordinate order, handle any vertical case before division, test whether a point from one line lies on the other, and combine direction with distinctness for the classification.

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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 parallelism