Imagine you draw a straight line down the middle of a piece of paper. This line is the line of symmetry. Anything you draw on one side of the line is going to have a mirror image on the other side of the line that looks exactly the same.
Now, if you have a point on the line of symmetry, that means the point is exactly in the middle of the line. And since the line is the same on both sides, that means the point is going to be the same on both sides too! So, the point on the line of symmetry stays in the same place and looks the same on both sides of the line.
- Dante