To find a point on x -axis. Therefore, its y -coordinate will be 0 . Let the point on x -axis be (x,0) . Consider A=(x,0);B=(2,−5) and C=(−2,9) .​AB=(2−x)2+(−5−0)2​=(2−x)2+25​AC=(−2−x)2+(9−0)2​=(−2−x)2+81​​ Since both the distance are equal in measure, so AB=AC .(2−x)2+25​=(−2−x)2+81​ Simplify the above equation,Remove square root by taking square both the sides, we get​(2−x)2+25=[−(2+x)2]+81(2−x)2+25=(2+x)2+81x2+4−4x+25=x2+4+4x+818x=25−81=−56x=−7​ Therefore, the point is (−7,0) .A(2,−5)