# Find a point on the X- axis which is equidistant from the points A (2, -5) and B (-2, 9).

Hint: We know that since the point is on X-axis, we have a point i.e, (x,0). Now let’s analyse the given condition and apply the distance formula. We’ll get the value of x which is only unknown in this condition.

Complete step by step answer:

The given points are A (2, -5) and B (-2, 9).

We need to find a point P which lies on the X-axis.

Let P be (x, 0).

As the distance between AP = AB, so we can use the distance formula

$\Rightarrow \sqrt {{{\left( {x - 2} \right)}^2} + {{\left( {0 - \left( { - 5} \right)} \right)}^2}} = \sqrt {{{\left( {x - \left( { - 2} \right)} \right)}^2} + {{\left( {0 - 9} \right)}^2}} $

Squaring both sides, we get,

$(x - 2)^2 +(0 -(- 5))^2 =(x -(- 2))^2 +(0 - 9)^2$

$\Rightarrow x^2 + 4 - 2x + 25 = x^2 + 4 + 2x + 81$

$\Rightarrow 4x = 25 - 81$

$\Rightarrow 4x = - 56 $

$ \Rightarrow x = - 14$

Therefore, P is (-14, 0).

Note: These types of questions are always based on the distance formula between two points. Always eliminate as many variables you can do in starting as if they are left for the end then the equation becomes very untidy.