How this calculator works
Average each pair of endpoint coordinates to locate the three midpoints. Subtracting the midpoint coordinates cancels the shared vertex and leaves half of the third side vector, proving both parallelism and the length ratio. Joining all three midpoints creates a similar medial triangle with half the side lengths and one quarter of the area. Coordinate distances use metres internally and accept negative positions.
Formula
M=(A+B)/2; N=(A+C)/2; N-M=(C-B)/2. Midsegment=BC/2; BC=2×midsegment; medial area=original area/4.
Worked example
For A=(0,0), B=(6,0), C=(0,8) in metres, M=(3,0) and N=(0,4). BC is 10 m and MN is 5 m. The original area is 24 m² and the medial area is 6 m².
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Frequently asked questions
Is a midsegment a median?
A midsegment joins two side midpoints. A median joins a vertex to the opposite midpoint.
Can I solve without coordinates?
Yes. A parallel side fixes its midsegment at half its length, and a midsegment fixes the side at twice its length.
Why are collinear points rejected?
They have zero area and do not form a non-degenerate triangle.