Answer:
When we do a reflection of a point (x, y) about a given line, the distance between the point (x, y) and the line is invariant under the transformation.
In the case of reflection over x-axis we have:
T (x, y) => (x, -y)
In the case of reflection over the y-axis, we have:
T (x, y) => (-x, y)
Because these two lines are perpendicular, a reflection over the x-axis leaves the distance between the point and the y-axis invariant (and the same for the inverse case)
Then 4 statements that will always be true:
1) The distance between p' and the x-axis is the same as the distance between p and the x-axis.
2) The distance between p' and the y-axis is the same as the distance between p and the y-axis.
From 1 and 2, we get:
3) The distance between p' and the origin is the same as the distance between p and the origin.
4) As we have a reflection, p' can not be in the same quadrant than p, then p' can not lie on the first quadrant.
