Find the value of k, if the point P (0, 2)


Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).


The distance $d$ between two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by the formula


It is said that P(0,2) is equidistant from both A(3,k) and B(k,5).

So, using the distance formula for both these pairs of points we have

$A P=\sqrt{(3)^{2}+(k-2)^{2}}$

$B P=\sqrt{(k)^{2}+(3)^{2}}$

Now since both these distances are given to be the same, let us equate both.

$A P=B P$


Squaring on both sides we have,


$9+k^{2}+4-4 k=k^{2}+9$

$4 k=4$


Hence the value of ‘k’ for which the point ‘P’ is equidistant from the other two given points is.

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