Find the point that partitions a directed segment between two points in a given ratio.
Apply the partition formula with algebraic coordinates
Problem
Use algebraic coordinates to find the partition point for this setup: point \(\text{halfway}\) from \((0,0)\) to \((2a,2b)\).
Big Picture
What this problem is really about
The partition formula works the same way with symbolic coordinates as with numbers. We’ll write the midpoint structure, average the two x-expressions and two y-expressions separately, simplify each coordinate without dropping a factor, and verify that the algebraic displacement before the point matches the displacement after it.
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