Question

1. figure q was the result of a sequence of transformations on figure p, both shown below. which sequence of transformations could take figure p to figure q? a. reflection over the x - axis and translation 7 units right b. reflection over the y - axis and translation 3 units down c. translation 1 unit right and 180° rotation about the origin d. translation 4 units right and 180° rotation about the origin

Explanation:

Step1: Analyze reflection

If we reflect figure $P$ over the $x - axis$, the $y$-coordinates of all points on figure $P$ change their signs.

Step2: Analyze translation

The left - most $x$-coordinate of figure $P$ is around $x=-5$ and the left - most $x$-coordinate of figure $Q$ is around $x = 2$. A translation of 7 units to the right after reflection over the $x$-axis will move figure $P$ to the position of figure $Q$.
For option B, reflection over the $y$-axis changes the $x$-coordinates' signs and translation 3 units down is not correct for getting from $P$ to $Q$. For option C, translation 1 unit right and 180 - degree rotation about the origin does not match the transformation. For option D, translation 4 units right and 180 - degree rotation about the origin also does not match.

Answer:

A. reflection over the $x$-axis and translation 7 units right