Question

find the point on x-axis which is equal distance from the point (5,-2) and (-3,2)

Answer 1

let the co-ordinates of the point
   which is equal distance from
        the point (5,-2) and (-3,2)    ⇒  (x,0)

co-ordinates of point A                =  (5,-2)
co-ordinates of point B                =  (-3,2)
co-ordinates of point p                 = (x,0)

AP²  =   BP²
using distance formula.........

(√(x-5)² + (0+2)²) ²             =   (√(x+3)² + (0-2)²)²
x² + 25 -10x+ 4                  =    x²+ 9 + 6x + 4
                           16x         =      16
                               x         =       1

∴ co-ordinate of point p    =   (1,0)            

                          

Answer 2

hey dear

here is your answer

Let the point p on x axis is ( x, 0)

we take distance from origin ( PA to PB)

it means PA square = PB square

The distance between p( x1, y1) and Q ( x2,y2)

so we use the formula of equal distance

$\sqrt{(x2 - x1) ^{2} } + \sqrt{(y2 - y1) {2} }$

we use this formula for equal distance

so

next step solution is attached

Answer comes (0,-2)


hope it helps

thank you