WAEC 2017 · Paper 2 · Q7

(a)
A parallelogram $MNQR$ has vertices $M(4, -6)$ , $N(10, 2)$ , $Q(8, 16)$ and $R(x, y)$ . Find the coordinates of $R$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

In $MNQR$ , $\overrightarrow{MN} = \overrightarrow{RQ}$ .
$\overrightarrow{MN} = \begin{pmatrix} 10 - 4 \\ 2 + 6 \end{pmatrix}$
$= \begin{pmatrix} 6 \\ 8 \end{pmatrix}$ and $\overrightarrow{RQ} = \begin{pmatrix} 8 - x \\ 16 - y \end{pmatrix}$ .
So $8 - x = 6$ and $16 - y = 8$ : $R(2, 8)$ .