1. For triangle ABC, what would be the equation of median AD if co-ordinates of A, B and C are (-5,4), (-4,0) and (-2,2) respectively?
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By: anil on 05 May 2019 02.16 am
Co-ordinates of triangle ABC are A(-5,4), B(-4,0) and C(-2,2) Median AD will bisect BC at D and D will be the mid point of BC. Thus, coordinates of D are = $$(frac{-4-2}{2},frac{0+2}{2})$$ = $$(frac{-6}{2},frac{2}{2}) = (-3,1)$$ 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(-5,4)and D(-3,1) is : => $$(y-4) = frac{(1-4)}{(-3+5)}(x+5)$$ => $$(y-4) = frac{-3}{2}(x+5)$$ => $$2y-8=-3x-15$$ => $$3x+2y=-7$$ => Ans - (C)
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