Question 1058619
Since the abscissa and ordinate of the unknown point are the same, the point
can be represented by (x, x).

The distance from (7, -3) to (x, x) is given by:


{{{d^2 = (7 - x)^2 + (x + 3)^2}}}


{{{d^2 = 49 - 14x + x^2 + x^2 + 6x + 9}}}


{{{d^2 = 2x^2 - 8x + 58}}}


Since the distance is equal to √58, we can write:


{{{(sqrt(58))^2 = 2x^2 - 8x + 58}}}


{{{58 = 2x^2 - 8x + 58}}}


{{{2x^2 - 8x = 0}}}


{{{2x(x - 4) = 0}}}


This gives solutions of x = 0 and x = 4.


Solution: There are two such points: (0, 0) and (4, 4)