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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