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4-66.

On graph paper, graph quadrilateral $MNPQ$ if $M(–3, –8), N(2, –10), P(1, –7),$ and $Q(–4, –5)$. $MNPQ$ is a parallelogram, which means that it has two pairs of parallel sides.

1. Show that $MNPQ$ is, indeed, a parallelogram.

2. Use the function $(x \rightarrow x, y \rightarrow -y)$ to reflect $MNPQ$ across the $x$-axis, creating $M^\prime N^\prime P^\prime Q^\prime$. What are the coordinates of $P^\prime$?

3. Name a different sequence of rigid transformations (one that is not the same as part (b) above) that will take $M^\prime N^\prime P^\prime Q^\prime$ back onto $MNPQ$.

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