The coordinates of the point on X-axis which are equidistant

Question:

The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are

(a) $(20,0)$

(b) $(-23,0)$

(c) $\left(\frac{4}{5}, 0\right)$

(d) None of these

Solution:

Let the point be A be equidistant from the two given points P (−3, 4) and Q (2, 5).

So applying distance formula, we get,

$\mathrm{AP}^{2}=\mathrm{AQ}^{2}$

Therefore,

$(a+3)^{2}+(-4)^{2}=(a-2)^{2}+5^{2}$

$10 a=4$

 $a=\frac{2}{5}$

Hence the co-ordinates of $A$ are $\left(\frac{2}{5}, 0\right)$

So the answer is- (D) none of these.

 

 

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