If the point P(k − 1, 2) is equidistant from the points A(3, k) and B(k, 5),


If the point P(k − 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.


The given points are P(k − 1, 2), A(3, k) and B(k, 5).

$\because A P=B P$

$\therefore A P^{2}=B P^{2}$



$\Rightarrow k^{2}-8 y+16+4+k^{2}-4 k=1+9$

$\Rightarrow k^{2}-6 y+5=0$


$\Rightarrow k=1$ or $k=5$

Hence, k = 1 or k = 5.


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