Q29 of 47 Page 1

A (4, -6), B (3, -2) and C (5, 2) are the vertices of ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas.


⸪ AD is the median, D is the mid-point of B and C.


Co-ordinates of D = =


Area of triangle (x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2))


⸫ Area of ΔABD =


= = 3 sq. units


⸫ Area of ΔADC =


= = 3 sq. units


⸫ ar (ΔABD) = ar (ΔADC) = 3 sq. units


⸫ The median divides the triangle into two equal areas.


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