First, let's change the coordinates using the translation [tex](x,y) \rightarrow (x+7, y)[/tex]
[tex]A:(-2,-5)[/tex]
[tex](-2,-5) \rightarrow (-2+7,-5)[/tex]
[tex]=(5,-5)[/tex]
Now, let's reflect this across the horizontal line y=2.
The y-term in the point is -5. That is 7 units down from y=2. Now, add 7 units to 2. You get 9. Change the y-term to this number.
[tex](x,y) \rightarrow (x,9)[/tex]
[tex](5,5) \rightarrow (5,9)[/tex]
(5, 9) is your answer. Hope this helps! :)
