Find the slope of a line, which passes through the origin, and the mid-point of
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) and B (8, 0).

Solution:

The coordinates of the mid-point of the line segment joining the points

$P(0,-4)$ and $B(8,0)$ are $\left(\frac{0+8}{2}, \frac{-4+0}{2}\right)=(4,-2)$

It is known that the slope $(m)$ of a non-vertical line passing through the points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, x_{2} \neq x_{1}$

Therefore, the slope of the line passing through (0, 0) and (4, –2) is

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

Hence, the required slope of the line is $-\frac{1}{2}$