Find the point that partitions a directed segment between two points in a given ratio.
Use partition points in a real-world context
Problem
In this context, what are the coordinates of the point? A rest stop is \(\text{one}\text{-}\text{third}\) of the way from town \(A(0,0)\) to town \(B(9,6)\).
Big Picture
What this problem is really about
The context identifies both a starting location and a fraction of the route completed. We’ll translate that language into a directed segment, compute the full coordinate displacement to the destination, scale both components by the progress fraction, add from the start, and compare completed and remaining route vectors as a check.
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