Question

find the point on the x-axis axis which is equidistant from (2,-5) (-2,9)​

Answer 1

Given:-

Two points A(2,5) and B(-2,9)

To find:-

The point on x-axis which is equidistant from both the given points.

Solution:-

Let the required point be P

Since, the point lies on the x-axis,

∴ the coordinates of the point must be P(x,0)

Since, P is equidistant from A and B,

∴ AP = BP

Using the distant formula,

$\sqrt{(x-2)^2+(0-5)^2}=\sqrt{[x-(-2)]^2+(0-9)^2}$

Squaring the both sides, we get,

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

Opening the brackets, we get,

$x^2 +4-2(x)(2) + 25 = x^2+4+2(x)(2) +81$

⇒ $4+-4x+25=4+4x+81$

⇒ $4x+4x = 81-25$

⇒ $8x= 56$

⇒ $x = \frac{56}{8} =7$

Hence, the required point is (7,0)