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Question

Find a point on the x-axis, which is equidistant from the points (5, 4) and (2, 3).


A

(152,0)

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B

(143,0)

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C

(277,0)

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D

(103,0)

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Solution

The correct option is B

(143,0)


Let point (x,0) is the point on the x-axis that is equidistant from the points (5, 4) and (2, 3).

Accordingly,

(5x)2+(40)2=(2x)2+(30)2

Squaring on both sides, we get,

52+x210x+16=4+x24x+9

4110x=134x

6x=28

x=143

Thus, required point on the x-axis is (143,0)


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