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).

Answer 1

Mid point of the line segment joining the points P(0, –4) and B(8, 0)

${\displaystyle \text{x}=\frac{{\text{x}}_1+{\text{x}}_2}{2}}$

= ${\displaystyle \frac{0+8}{2}}$

= 4

y = ${\displaystyle \frac{{\text{y}}_1+{\text{y}}_2}{2}}$

= ${\displaystyle \frac{-4+0}{2}}$

= ${\displaystyle \frac{-4}{2}}$

= −2

= The midpoint of PB has coordinates (4, −2) of M.

The coordinates of the origin point 0 are (0, 0).

∴ OM = ${\displaystyle \frac{{\text{y}}_2-{\text{y}}_1}{{\text{x}}_2-{\text{x}}_1}}$

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

= ${\displaystyle \frac{-2}{4}}$

= ${\displaystyle \frac{-1}{2}}$