Since the required point (say P) is on the X-axis, its ordinate will be zero. Let the abscissa of the point be x.
Therefore, coordinates of the point P are (x, 0).
Let A and B denote the points (5, 4) and (-2, 3), respectively.
Since we are given that AP = BP, we have AP2 = BP2
i.e., (x - 5)2 + (0 - 4)2 = (x + 2)2 + (0 - 3)2
or x2 + 25 - 10x + 16 = x2 + 4 + 4x + 9 or -14x = - 28 or x = 2
Thus, the required point is (2, 0).