Problem preview

G-GPE.6 Warmup M2-044-A04-V02

Find the point that partitions a directed segment between two points in a given ratio.

Interpret and compute a directed segment partition

Problem

Interpret and compute this directed internal partition: start \(B=(9,6)\), end \(A=(0,0)\), internal ratio \(BP:PA=1:2\).

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P = (6, 4), because 1:2 places P one-third of the way from B to A.

P = (3, 2), because 1:2 places P two-thirds of the way from B to A.

P = (3, 2), and reversing the endpoints gives the same point.

P = (12, 8), using B − A as the displacement from B.

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Curriculum context

Course: Math II
Standard: G-GPE.6
Category: Geometry
Domain: Expressing Geometric Properties with Equations
Objective: Find the point that partitions a directed segment between two points in a given ratio.
Problem type: Interpret and compute a directed segment partition