WAEC 2019 · Paper 2 · Q8

Vectors

(a)
$A(-3, 1)$ , $B(1, 2)$ , $C(0, -1)$ and $D(x, y)$ are the vertices of a parallelogram $ABCD$ . Using the vector method, determine the coordinates of $D$ .
Separate values with commas, e.g. 3, −2

Try it on a graph

The parallelogram ABCD.

Worked solution (try it first)

In $ABCD$ , $\overrightarrow{AB} = \overrightarrow{DC}$ , so $\mathbf d = \mathbf a + \mathbf c - \mathbf b$ .
$\mathbf d = \begin{pmatrix} -3 + 0 - 1 \\ 1 - 1 - 2 \end{pmatrix}$
$= \begin{pmatrix} -4 \\ -2 \end{pmatrix}$ .
So $D(-4, -2)$ .

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