Hello,

1. make a sketch. Place some points with the required property and you'll see immediately:

What is the locus of points in the plane of an angle that are equidistant from the sides of the angle? = angle bisector

What is the locus of points in space that are equidistant from two parallel planes? = mid plane

What is the locus of points in a plane that are equidistant from points A and B in the plane? = perpendicular bisector of the distance AB

(not sure that I used the appropriate expressions)