Question

In $\Delta$ABC, $A(3,5),B(7,8)$ and $C(1,-10)$. Find the equation of the median through $A$.

Answer 1

Here $D$ is mid point of $BC$.
$\therefore$ The co-ordinate of D$=\left(\frac{7+1}{2},\frac{8-10}{2}\right)$
$=(4,-1)$
Now equation of median $AD$,
$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$
Here, $x_1=3,y_1=5,x_2=4,y_2=-1$
$y-5=\frac{-1-5}{4-3}(x-3)$
$y-5=\frac{-6}{1}(x-3)$
$y-5=-6x+18$
$y=-6x+18+5$
$y=-6x+23$
$6x+y-23=0$