Problem preview
G-GPE.6 Warmup M2-044-A05-V01

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

Find a missing endpoint from a partition point

Problem

Find the missing endpoint when \(A(0,0)\) and partition point \(M(3,4)\) are given, and \(M\) is the midpoint of \(AB\).

Big Picture

What this problem is really about

Finding a missing endpoint reverses the partition relation instead of stopping at the known interior point. We’ll solve the midpoint average for the unknown endpoint, substitute coordinatewise, interpret the result as continuing the same half-segment displacement beyond the midpoint, and average the recovered endpoints to check the original condition.

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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 missing endpoint from a partition point