WAEC 2018 · Paper 2 · Q9

(a)
Points $L(-1, 0)$ , $M(3, 7)$ and $N(5, -2)$ are the midpoints of the sides $BC$ , $CA$ and $AB$ respectively of triangle $ABC$ . Find the equation of line $AB$ .
Show the answer
$4y - 7x + 43 = 0$

Worked solution (try it first)

The line joining the midpoints of two sides is parallel to the third side, so $LM \parallel AB$ .
Gradient of $LM$ : $\dfrac{7 - 0}{3 + 1} = \dfrac74$ .
$AB$ passes through its own midpoint $N(5, -2)$ : $y + 2 = \frac74(x - 5)$ .
$4y + 8 = 7x - 35$ , so $4y - 7x + 43 = 0$ .