Question

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points $P(0,–4)\text{and}B(8,0)$.

Answer 1

Slope of line
Given $P(0,-4)\&B(8,0)$
Let $M$ be the midpoint of $P(0,-4)\&B(8,0)$

We know that midpoint of $(x_1,y_1)\&(x_2,y_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
Mid point $M$ of $(0,-4)\&(8,0)$
$=(\frac{0+8}{2},\frac{-4+0}{2})=(\frac{8}{2},\frac{-4}{2})=(4,-2)$
So, the line should pass through $M(4,-2)$ and $O(0,0)$
We know that slope of line passing through $(x_1,y_1)\text{and}(x_2,y_2)\text{is}m=\frac{y_2-y_1}{x_2-x_1}$
Here, $x_1=0,y_1=0\text{and}$
$x_2=4,y_2=-2$
Slope of line between points $O(0,0)\&M(4,-2)=m=\frac{-2-0}{4-0}=\frac{-2}{4}=\frac{-1}{2}$
Hence, slope of line is $\frac{-1}{2}$