We are looking for the locus of points that are equidistant from the points (1,3) and (5,6).
We know that the Midpoint is equidistant between these two ordered pairs; however, are there any other points also in the locus? YES!
Move point C...as you do so, the locus described above will be traced.
Notice that all the points in this locus form a straight line.
Moreover, notice that the distance between (1,3) and point C is equidistant to the distance between (5,6) and point C.