Question

Find the slope of a line, which passes through the origin, and the mid-points of the line segments joining the points $P(0,-4)$ and $B(8,0)$.

Answer 1

We need to find slope of a line passing through origin $O(0,0)$ and mid-point of $P(0,-4)$ and $B(8,0)$

Let $M$ be the mid-point of $P(0,-4)$ and $B(8,0)$

We know that,

Mid-point of $(x_1,y_1)$ and $(x_2,y_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Mid-point $M$ of $(0,-4)$ and $8,0)=(\frac{0+8}{2},\frac{-4+0}{2})$

$=(\frac{8}{2},\frac{-4}{2})$

$=(4,-2)$

We know that slope of line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of the line between points $O(0,0,)$ and $M(4,-2)$

Here, $x_1=0,$ $y_1=0$

$x_2=4,$ $y_2=-2$

$m=\frac{-2-0}{4-0}=\frac{-2}{4}=\frac{-1}{2}$

Hence, slope of line its $\frac{-1}{2}$