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?

Answer: Option A

Co-ordinates of mid point (D) which lies on the line BC = $$\left(\frac{3+5}{2},\frac{0-2}{2}\right)=\left(4,-1\right)$$
Now, Co-ordinates of line AD = A(2, -4), D(4, -1)
∴ Equation of the line which passes through the two point (x₁, y₁), & (x₂, y₂)
⇒ y - y₁ = m(x - x₁)
∴ required equation of the line
= y + 4 = m(x - 2)
$$\begin{array}{rl}& \left[\because m=\frac{y_2-y_1}{x_2-x_1}\right]\\ & \therefore m=\frac{-1+4}{4-2}=\frac{3}{2}\\ & \Rightarrow y+4=\frac{3}{2}\left[x-2\right]\\ & \Rightarrow 2y+8=3x-6\\ & \Rightarrow 3x-2y=14\end{array}$$