Problem preview
G-GPE.6 Warmup M2-044-A03-V01

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

Find a point that partitions a directed segment in a ratio

Problem

Find the point that partitions the directed segment from \((0,0)\) to \((10,5)\) in the ratio \(1:4\).

Big Picture

What this problem is really about

An internal ratio first has to become a fraction traveled from the ordered starting endpoint. We’ll add the ratio parts for the total, use the first part as the traveled fraction, scale the full start-to-end displacement componentwise, add from the start, and verify the two subsegment vectors have the requested scale.

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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 a point that partitions a directed segment in a ratio