Question

find a point on x axis which is equidistant from (-2,5) and (2,3)​

Answer 1

Solution

let the point is (X,O)

as the point is lying on the X axis so it's abcissa is zero.(y=0)

now...

the point (X,0)is equidistant from the points (-2,5);(2,3)

therefore...

$\sqrt{(x + 2) {}^{2} + (0-5) {}^{2} } = \sqrt{(2 - x) {}^{2} + (3 - 0) {}^{2} } \\ = > (x + 2) {}^{2} + 25 = (2 - x) {}^{2} + 9 \\ = > x {}^{2} + 4x + 4 + 16 = 4 - 4x + x {}^{2} \\ = > 4x + 20 = 4 - 4x \\ = > 8x = - 16 \\ = > x = - 2$

therefore the point is (-2,0).

Hope this helps you........