A(7, -3), B(5, 3) and C(3, -1) are the vertices of a \Delta ABC an | Filo
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Coordinate Geometry

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and are the vertices of a and AD is its median. Prove that the median AD divides into two triangles of equal areas.

Solution:
D is midpoint of BC, so find its coordinates using below:
Midpoint formula:
Find area of triangle ABD:
We know that:
Area of a triangle
So,
Area of triangle ABD:
sq. units .......
Area of triangle ACD:
sq. units ........
From and , we conclude that Area of triangle ABD and ACD is equal.
Hence proved.
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