find a point equidistant from
the points (3,1) and (5,6) ,if its abscisaa is equal to its ordinate.
such a point will lie on the perpendicular bisector of the line between the two points. Since the slope of that line is 5/2, your point will lie on the line
y - 7/2 = -2/5 (x-4)
A point on that line with equal x- and y-coordinates will be
x - 7/2 = -2/5 (x-4)
or,
(51/14,51/14)