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Question

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

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Solution

Let the point on the x-axis be B(x,0).

The point is equidistance from the point A(2,5) and C(2,9).

Then,

AB2=BC2

(x2)2+(0+5)2=(x+2)2+(09)2

x24x+4+25=x2+4x+4+81

8x=56

x=7

The point on the x axis is (7,0).


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