Question

reflect quadrilateral qrst over the x - axis. then, reflect its image, quadrilateral qrst, over the y - axis.
original point\tpoints after reflection over x - axis
q\t(-5,-1)\tq
r\t(-1,-1)\tr
s\t(-1,-3)\ts
t\t(-6,-3)\tt

Explanation:

Step1: Recall x - axis reflection rule

The rule for reflecting a point $(x,y)$ over the $x$-axis is $(x,-y)$.

Step2: Reflect point Q

For $Q(-5, - 1)$, after reflection over the $x$-axis, $Q'=(-5,1)$ since $x=-5$ and $y = - 1$ gives $-y=1$.

Step3: Reflect point R

For $R(-1,-1)$, after reflection over the $x$-axis, $R'=(-1,1)$ as $x=-1$ and $-y = 1$.

Step4: Reflect point S

For $S(-1,-3)$, after reflection over the $x$-axis, $S'=(-1,3)$ because $x=-1$ and $-y = 3$.

Step5: Reflect point T

For $T(-6,-3)$, after reflection over the $x$-axis, $T'=(-6,3)$ since $x=-6$ and $-y = 3$.

Step6: Recall y - axis reflection rule

The rule for reflecting a point $(x,y)$ over the $y$-axis is $(-x,y)$.

Step7: Reflect Q' over y - axis

For $Q'(-5,1)$, after reflection over the $y$-axis, $Q''=(5,1)$ as $-x = 5$ and $y = 1$.

Step8: Reflect R' over y - axis

For $R'(-1,1)$, after reflection over the $y$-axis, $R''=(1,1)$ since $-x = 1$ and $y = 1$.

Step9: Reflect S' over y - axis

For $S'(-1,3)$, after reflection over the $y$-axis, $S''=(1,3)$ because $-x = 1$ and $y = 3$.

Step10: Reflect T' over y - axis

For $T'(-6,3)$, after reflection over the $y$-axis, $T''=(6,3)$ as $-x = 6$ and $y = 3$.

Answer:

The final points after both reflections: $Q''(5,1)$, $R''(1,1)$, $S''(1,3)$, $T''(6,3)$