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?

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)