If `A(4,-6),B(3,-2)a n dC(5,2)` are the vertices of ` A B C ,` then verify the fact that a median of a triangle ABC divides it into two triangles of equal areas.

Explanation

Let D be the mid- point of BC. Then, the coordinates of D are (4, 0).


`Area of ΔABC = 1/2 |(4 × (-2) + 3 × 2 + 5 × (-6)) - (3 × (-6) + 5 × (-2) + 4 × 2)|`


`⇒ Area of ΔABC = 1/2|(-8 + 6 - 30) - (-18 - 10 + 8)|`


`⇒ Area of ΔABC = 1/2|-32 + 20| = 6 sq. units`


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