​Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9):​

Correct option is A

Given:
​$$A(2, -5), \; B(-2, 9) \\$$​​
Required point lies on x-axis:  (x, 0)
Concept used:
Equidistant condition:
​$$\sqrt{(x-2)^2 + (0+5)^2} = \sqrt{(x+2)^2 + (0-9)^2} \\[8pt]$$​​
Solution:
​$$(x-2)^2 + 25 = (x+2)^2 + 81 \\[4pt]x^2 -4x +4 +25 = x^2 +4x +4 +81 \\[4pt]-4x +29 = 4x +85 \\[4pt]-4x -4x = 85 -29 \\[4pt]-8x = 56 \implies x = -7 \\[8pt]$$​​
Required point: (-7, 0)
Correct answer is (A) (–7, 0)