Question

The vertices of $△ABC$ are $A(2,1),B(-2,3)$ and $C(4,5)$. Find the equation of the median through the vertex $A$.

Answer 1

Let $A(2,1),B(-2,3),C(4,5)$ be vertices of $△ABC$ and $AD$ be the median.

$D$ be mid point of $BC$.

$D=(\frac{-2+4}{2},\frac{3+5}{2})$

$\Rightarrow D=(1,4)$

Now $A(2,1)\equiv (x_2,y_2)andD(1,4)\equiv (x_1,y_1)$

The equation of median $AD$ is

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

$\Rightarrow \frac{y-4}{1-4}=\frac{x-1}{2-1}$

$\Rightarrow \frac{y-4}{-3}=\frac{x-1}{1}$

$\Rightarrow -3x+3=y-4$

$\Rightarrow 3x-3+y-4=0$

$\Rightarrow 3x+y-7=0$