For triangle ABC, find equation of median AD if co-ordinates of points A, B and C are (2,-4), (3,0) and (5,-2) respectively? ?->(Show Answer!)

1. For triangle ABC, find equation of median AD if co-ordinates of points A, B and C are (2,-4), (3,0) and (5,-2) respectively?

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By: anil on 05 May 2019 02.15 am

Co-ordinates of triangle ABC are A(2,-4), B(3,0) and C(5,-2) Median AD will bisect BC at D and D will be the mid point of BC. Thus, coordinates of D are = $$(frac{3+5}{2},frac{0-2}{2})$$ = $$(frac{8}{2},frac{-2}{2}) = (4,-1)$$ Now, equation of line passing through $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is : $$(y-y_1) = frac{y_2-y_1}{x_2-x_2} (x-x_1)$$ => Equation of AD where A(2,-4)and D(4,-1) is : => $$(y+4) = frac{(-1+4)}{(4-2)}(x-2)$$ => $$(y+4) = frac{3}{2}(x-2)$$ => $$2y+8=3x-6$$ => $$3x-2y=14$$ => Ans - (A)

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