Question

If the coordinates of the vertices of the triangle $ABC$ be $(-1,6),(-3,-9)$, and $(5,-8)$ respectively, then the equation of the median through $C$ is

• A. $13x-14y-47=0$
• B. $13x-14y+47=0$
• C. $13x+14y+47=0$
• D. $13x+14y-47=0$

Answer 1

The correct option is A $13x-14y-47=0$

Let the Median be $CD$

Point of $D$ is $(x,y)$

Now,

$x=\frac{-3-1}{2},x=-2$ and $y=\frac{6-9}{2}=-\frac{3}{2}$

Slope of CD is,

$=\frac{8-\frac{3}{2}}{5+2}=\frac{13}{14}$

Equation:

$CD=y+8=\frac{13}{14}(x-5)$

So the equation of Median,

$13x-14y-47=0$