Question

in the coordinate plane, the points (x(-3, -7)), (y(5, 6)), and (z(2, -9)) are reflected over the (x)-axis to the points (x), (y), and (z), respectively. what are the coordinates of (x), (y), and (z)?

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected over the $x - axis$, the $x$-coordinate remains the same and the $y$-coordinate changes its sign, so the new point is $(x, -y)$.

Step2: Find $X'$

For point $X(-3,-7)$, applying the rule, the $x$-coordinate is $- 3$ and the new $y$-coordinate is $-(-7)=7$. So $X'(-3,7)$.

Step3: Find $Y'$

For point $Y(5,6)$, the $x$-coordinate is $5$ and the new $y$-coordinate is $-6$. So $Y'(5, - 6)$.

Step4: Find $Z'$

For point $Z(2,-9)$, the $x$-coordinate is $2$ and the new $y$-coordinate is $-(-9)=9$. So $Z'(2,9)$.

Answer:

$X'(-3,7)$
$Y'(5,-6)$
$Z'(2,9)$