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?

Solution (By Examveda Team)

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)
$$\eqalign{ & \left[ {\because m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right] \cr & \therefore m = \frac{{ - 1 + 4}}{{4 - 2}} = \frac{3}{2} \cr & \Rightarrow y + 4 = \frac{3}{2}\left[ {x - 2} \right] \cr & \Rightarrow 2y + 8 = 3x - 6 \cr & \Rightarrow 3x - 2y = 14 \cr} $$