Maths / Coordinate Geometry / Distance Formula

QUESTION

A point on x - axis which is equidistance from the points (3,4) and (2,5) is

 OPTIONS A. (2,0) B. (-2,0) C. (4,0) D. None of the above
Right Option : B

EXPLANATION
Explain TypeExplanation Content
Text

Let the point on x-axis be P(x,o) which is equidistance from A(3,4) and (2,5).

i.e.,                                  PA=PB

$\Rightarrow$             $\large \sqrt{(x-3)^2+(4-0)^2}=\sqrt{(x-2)^2+(5-0)^2}$

$\Rightarrow$                        $\large x^2-6x+9+16=x^2-4x+4+25$

$\Rightarrow$                                                          2x = -4 $\Rightarrow$ x = -2

Thus, point = (-2,0)

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