Answer :
The transformation rule for a reflection across the x-axis is:
[tex]A(x,y)\longrightarrow A^{\prime}(x,-y)[/tex]We will apply this rue to the three vertices.
Reflection across the x-axis of P:
[tex]P(-5,-7)\longrightarrow P^{\prime}(-5,-(-7))[/tex]In the image point, the x-coordinate remains the same, but we have to change the sign of the y-coordinate:
[tex]P(-5,-7)\longrightarrow P^{\prime}(-5,7)[/tex]Reflection across the x-axis of Q:
[tex]Q(-5,-2)\longrightarrow Q^{\prime}(-5,-(-2))[/tex]Simplifying the expression:
[tex]Q(-5,-2)\longrightarrow Q^{\prime}(-5,2)[/tex]Reflection across the x-axis of R:
[tex]R(-9,-10)\longrightarrow R^{\prime}(-9,-(-10))[/tex]simplifying the expression:
[tex]R(-9,-10)\longrightarrow R^{\prime}(-9,10)[/tex]Answer:
[tex]\begin{gathered} P(-5,-7)\longrightarrow P^{\prime}(-5,7) \\ Q(-5,-2)\longrightarrow Q^{\prime}(-5,2) \\ R(-9,-10)\longrightarrow R^{\prime}(-9,10) \end{gathered}[/tex]