Question

If equation of the perpendicular bisector of the line joining the points$(0,3)$ and $(-4,5)$ is $y=mx+8$. Find $m$

Answer 1

Equation of line-

$y=mx+c$; m = slope of line

Let $m^{\prime }$ be the slope of line joining the points $(0,3)\&(-4,0)$.

Slope of a line joining points $(x_1,y_1)\&(x_2,y_2)=\frac{y_2-y_1}{x_2-x_1}$

$\therefore$ Slope of line joining $(0,3)\&C(-4,5)=\frac{5-3}{-4-0}=\frac{2}{-4}=-\frac{1}{2}$

As the line $y=mx+8$ and the line joining the points $(0,3)\&(-4,0)$ are perpendicular to each other, product of their slope will be -1.

$m.m^{\prime }=-1$

$\Rightarrow m=\frac{-1}{m^{\prime }}$

$m=\frac{-1}{(-\frac{1}{2})}=2$

Hence, $m=2$.