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Question

Find a point on the x-axis which is equidistant from the points (7,6) and (3,4)

A
(3,0)
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B
(2,0)
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C
(3,0)
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D
(4,0)
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Solution

The correct option is A (3,0)

Let the point on the x-axis be (x,0).
Distance between (x,0) and (7,6)=(7x)2+(60)2=72+x214x+36=x214x+85
Distance between (x,0) and (3,4)=(3x)2+(40)2=9+x2+6x+16=x2+6x+25
As the point (x,0) is equidistant from the two points, both the distances calculated are equal.
x214x+85=x2+6x+25
x214x+85=x2+6x+25
8525=6x+14x
60=20x

x=3
Thus, the point is (3,0).


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