Question

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

Answer 1

Median is a straight line joining a vertex and the midpoint of the opposite side.
Let $D$ be the midpoint of $BC$.
$\therefore$ Midpoint of $BC$ is $D(\frac{-2+4}{2},\frac{3+5}{2})=D(1,4)$
Now the equation of the median $AD$ is
$\frac{y-1}{4-1}=\frac{x-2}{1-2}$
$\frac{y-1}{3}=\frac{x-2}{-1}$
$\therefore$ $3x+y-7=0$ is the required equation.