A line 'l' intersects line 'm' at point A at 45 degree angle. B and C are points on line m, where the distance from B to A is equal to the distance from A to C. How many points on line 'l' are equidistant from points B and C?

Question

How is it one point? And this one point on line 'l' is the point that intersects point A? I thought that points B and C are the same points, so if I drew a vertical line perpendicular to line 'm' then as long as the horizontal distance from point B or C to this other new point is equal, then can't there be an infinite amount of points? Because this new point can be anywhere on line 'l'?

Let me know your explanation because I think I may have not understood the question or drawn the diagram correctly.

Thanks!

Answer 1

I assume point A is on line l

Place B and C anywhere on line m
draw the perpendicular bisector of BC, and extend the line
Notice that no matter where you draw B and C, this right bisector will cut line l only once.
label that point A.
properties of this right bisector:
AB = AC