On the screen, we see two straight lines AB and CD in black color. We have drawn angle bisectors of these two lines in blue color. We took a free point F on this coordinate plane and drew perpendiculars (FH & FG) from this point F to the lines AB and CD. We know that the distance between a point and a line is the height of the perpendicular drawn from the point to the line thus FH and FG are the distances from this point F to the two lines. Now let us move the points A, B, C, D and F and observe how the length of the perpendiculars changes.

What do you observe when this point F lies on the angle bisectors (blue)?