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G-GPE.6 Warmup M2-044-A06-V04

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

Find the ratio in which a point partitions a segment

Problem

Point \(P~=~(2,~5)\) partitions the directed segment from \(A~=~(-1,~2)\) to \(B~=~(11,~14)\). Compare displacement \(AP\) with total displacement \(AB\), then give the internal ratio \(AP:PB\) in simplest form.

Neutral partition-ratio reference: start (negative 1, 2), point (2, 5), and end (11, 14), without a drawn segment or proportional lengths. Open full size
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Four variants of this problem type
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
Find the ratio in which a point partitions a segment