JAMB 1994 · UME · Q35

Coordinate geometry

If $M(4, q)$ is the midpoint of the line joining $L(p, -2)$ and $N(q, p)$ , find the values of $p$ and $q$ .

Worked solution (try it first)

The midpoint is the average of the ends.
For $x$ : $\frac{p + q}{2} = 4$ , so $p + q = 8$ .
For $y$ : $\frac{-2 + p}{2} = q$ , so $p - 2 = 2q$ and $p = 2q + 2$ .
Put this into $p + q = 8$ : $3q + 2 = 8$ , so $q = 2$ and $p = 6$ , option D.

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