JAMB 1995 · UME · Q30

Two perpendicular lines $PQ$ and $QR$ intersect at $(1, -1)$ . If the equation of $PQ$ is $x - 2y + 4 = 0$ , find the equation of $QR$ .

Worked solution (try it first)

Rearrange $PQ$ : $2y = x + 4$ , so $y = \frac12x + 2$ and its gradient is $\frac12$ .
Perpendicular gradients multiply to $-1$ , so $QR$ has gradient $-2$ .
$QR$ passes through $(1, -1)$ : $y - (-1) = -2(x - 1)$ , so $y + 1 = -2x + 2$ .
Collect terms on one side: $2x + y - 1 = 0$ , option D.