EXPLANATION:
We are given the following coordinates for a figure on the coordinate plane;
[tex]\begin{gathered} P(2,-12) \\ Q(-3,13) \\ R(-5,-15) \end{gathered}[/tex]
To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]
Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.
Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.
Therefore, for the vertices given, the reflection across the x-axis would be;
[tex]P(2,-12)\rightarrow P^{\prime}(2,12)[/tex][tex]Q(-3,13)\rightarrow Q^{\prime}(-3,-13)[/tex][tex]R(-5,-15)\rightarrow R^{\prime}(-5,15)[/tex]
ANSWER:
The coordinates of the reflection across the x-axis therefore will be;
[tex]\begin{gathered} P^{\prime}(2,12) \\ Q^{\prime}(-3,-13) \\ R^{\prime}(-5,15) \end{gathered}[/tex]
