Question

Find the slope of the line which passes through the origin and the midpoint of the line segment joining the points $P(0,-4)andB(8,0)$

Answer 1

Finding the slope of the line:

First we will, determine the midpoint of the line $PB$ using the formula :

Midpoint $(x,y)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Midpoint of line $PB$ joining the points $P(0,-4)andB(8,0)$ is given as

Midpoint$=(\frac{0+8}{2},\frac{-4+0}{2})$

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

$\Rightarrow$Midpoint$=(4,-2)$

Now, the slope$\left(m\right)$ of a line is given as

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

As the line is passing through the origin$(0,0)$ then the slope will be

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

$\Rightarrow m=\frac{-1}{2}$

Hence, the slope of the line which passes through the origin and the midpoint of the line segment joining the points $P(0,-4)andB(8,0)$ is $\frac{-1}{2}$