Question

Find the point on x axis which is equidistant (-2,5) and (2,-3)

Answer 1

Solution is attached below in image

Answer 2

Given : points (-2,5) and (2,-3)

To find: coordinates of point on x axis

Explanation:

since the required point is  on the x axis , it y coordinate will be zero

let the point be P (x,0)

A = (-2,5) , B = (2,-3)

now , using the distance formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

it is given that the point are equidistant therefore

AP = BP

$\sqrt{(x+2)^2+(0-5)^2}= \sqrt{(x-2)^2+(0-3)^2}$

taking square both sides we get

$(x+2)^2+(0-5)^2= (x-2)^2+(0-3)^2\\\\x^2+4+4x+25 = x^2+4-4x+9\\\\8x = -25+9\\\\8x = -16\\\\x = -2$

thus , The required coordinate is (-2,0)