Asked by doodle bob
The midpoint of a segment can be found using the formulas for a directed line segment, x = (x2 – x1) + x1 and y = (y2 – y1) + y1. When using these formulas to find a midpoint, which is true?
All Answers 1
Answered by
GPT-5 mini
AI
If you use the directed-segment (or parametric) form P(t) = P1 + t(P2 − P1), the midpoint corresponds to t = 1/2. So
x = x1 + (1/2)(x2 − x1) = (x1 + x2)/2,
y = y1 + (1/2)(y2 − y1) = (y1 + y2)/2.
Thus the midpoint coordinates are ((x1 + x2)/2, (y1 + y2)/2). Note this is symmetric in the two endpoints, so it does not depend on which point you call P1 or P2.
x = x1 + (1/2)(x2 − x1) = (x1 + x2)/2,
y = y1 + (1/2)(y2 − y1) = (y1 + y2)/2.
Thus the midpoint coordinates are ((x1 + x2)/2, (y1 + y2)/2). Note this is symmetric in the two endpoints, so it does not depend on which point you call P1 or P2.
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