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

The coordinates of the mid-point of the line segment joining the points P (0, -4) and B (8, 0) are:
$(\frac {0+8}{2},\frac {-4+0}{2}) = (4,-2)$
It is known that the slope (m) of a non-vertical line passing through the points (x1, y1) and (x2, y2) is given by:
$m = \frac {y_2-y_1}{x_2-x_1}, \ x_2≠x_1$
Therefore, the slope of the line passing through (0, 0) and (4, -2) is:
$\frac {-2-0}{4-0 }= -\frac {2}{4} = -\frac 12$
Hence, the required slope of the line is $-\frac 12$.