WAEC 2017 · Paper 2 · Q3

(a)
A line is parallel to $2x + 3y = 5$ . If the line is the perpendicular bisector of the line joining the points $(3, y)$ and $(5, 2)$ , find its equation.
Show the answer
$6y + 4x - 19 = 0$

Worked solution (try it first)

$2x + 3y = 5$ has gradient $-\frac23$ , so the bisector has gradient $-\frac23$ too (parallel).
The segment is perpendicular to it, with gradient $\frac32$ : $\dfrac{2 - y}{5 - 3} = \dfrac32$ , so $y = -1$ .
The midpoint of $(3, -1)$ and $(5, 2)$ is $\left(4, \frac12\right)$ .
$y - \frac12 = -\frac23(x - 4)$ .
Multiply by 6: $6y - 3 = -4x + 16$ .
So $6y + 4x - 19 = 0$ .