There is something wrong with your question, because there are countless points, not one point, that are equidistant from two points. Of course, these points are all on the same straight line, which is the vertical line between two known points.

As shown in the figure: Let two known points be A and B, and draw with compasses. Take A and B as the center and the distance of AB as the radius. The two circles intersect C and D respectively, and the distances from any point on the straight line CD to A and B are equal.