Apply geometric motions to reflect figures. Brianna reflects point P over a line of reflection, resulting in point P'.

Question

If points P and P' have the same y coordinate, what must be true?

Answer 1

If points \( P \) and \( P' \) have the same y-coordinate after point \( P \) is reflected over a line of reflection, this means that the line of reflection is a horizontal line. When a point is reflected over a horizontal line, the y-coordinates of the original point and its reflection will remain the same, while the x-coordinates may change. This situation occurs because reflection results in points that are equidistant from the line of reflection.

Therefore, if points \( P \) and \( P' \) have the same y-coordinate, we can conclude that the line of reflection must be horizontal.