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?

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)