Answer for the first box: y = 0
Answer for the second box: y = x+1
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Explanation:
The line y = 0 is the horizontal line that overlaps the x axis perfectly. If the line of reflection is y = 0, then you reflect over the x axis to have F = (6,3) move to F' = (6,-3). The perpendicular bisector of FF' is y = 0, which is exactly the line of reflection. Point E is on the line y = 0.
Now create any line you want that does not go through point E. One such line is y = x+1. This line of reflection will play the role as the perpendicular bisector of FF'. Point E is not on the line because plugging x = 0 does not lead to y = 0, and instead it leads to y = 1.
So as you can see, Kari's claim is not 100% correct as there are counter-examples to show it doesn't always work.
