Review question

# Can we show that $OAQY$ is a parallelogram? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8704

## Question

Note; this figure is not intended to be completely accurately drawn.

In the figure the points $X$ and $Y$ are such that $AX = \dfrac{1}{2}XB$ and $OY = YX$, while the point $P$ is such that $OA = 3AP$. The lines $YQ$ and $PQ$ are parallel to $OA$ and $OB$ respectively.

Given that $\mathbf{OA} = \mathbf{a}$ and $\mathbf{OB} = \mathbf{b}$, express $\mathbf{OP}$ and $\mathbf{OY}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.

Given that $\mathbf{YQ} = m\mathbf{a}$ and $\mathbf{PQ} = n\mathbf{b}$, find the values of $m$ and $n$. Hence show that $OAQY$ is a parallelogram.