Let the point be X(x,0) and the other two points are given as A(2, – 5) and B(– 2,9)

Given XA = XB

By distance formula, as shown below:

XA = √{(2 – x)² + (– 5 – 0)²}

= √{(2 – x)² + (– 5)²}

= √{4 + x² – 4x + 25}

⇒ XA = √{29 + x² – 4x}

XB = √{(– 2 – x)² + (9 – 0)²}

= √{(– 2 – x)² + (9)²}

= √{4 + x² + 4x + 81}

⇒ XB = √{85 + x² + 4x}

Now since

XA = XB

Squaring both sides, we get,

(29 + x² – 4x) = (85 + x² + 4x)

56 = – 8x

x = – 7

The point on × axis is (– 7, 0)