Question

Find the point on the x axisvwhich is equidistant from (2,-5) and (-2,9)

Answer 1

I hope you got to know

Answer 2

The point on the x axis which is equidistant from (2, -5) and (-2, 9) is (-7 , 0)

Solution:

Given that,

We have to find the point on the x axis which is equidistant from (2,-5) and (-2,9)

From given,

The point is on the x axis

Thus the coordinate of the point is (h, 0)

Now

This point (h , 0) is equidistant from (2, -5) and (-2, 9)

Thus,

$(2-h)^{2} + (-5-0)^{2} = (h+2)^{2} + (0-9)^{2} \\\\Simplify\\\\2^2 + h^2 - 4h + 25 = h^2 + 4 + 4h + 81 \\\\-4h + 29 = 4h + 85 \\\\ -8h = 85-29\\\\ -8h = 56\\\\h = -7$

Thus the point on the x axis which is equidistant from (2,-5) and (-2,9) is (-7 , 0)

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