When a point is reflected over the x-axis, it is moved along a vertical line to the same distance on the other side of the x-axis.
The x-coordinate of a point identifies its distance from the y-axis--the vertical line it is on. The y-coordinate identifies its distance from the x-axis. Changing the sign of the y-coordinate moves the point to the same distance on the other side of the x-axis--reflecting it over the x-axis.
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The given points ABC and A'B'C' all match the pattern ...
(x, y) ⇒ (x, -y)
A(-1, 7) ⇒ A'(-1, -7)
B(6, 5) ⇒ B'(6, -5)
C(-2, 2) ⇒ C'(-2, -2)
so the image points represent a reflection over the x-axis of the original points.
