text: # Find the value of k, if the point P (0, 2)
  
  Question:
  
  Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
  
  Solution:
  
  The distance $d$ between two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by the formula
  
  $d=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}$
  
  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.
  
  $A P=B P$
  
  $\sqrt{(3)^{2}+(k-2)^{2}}=\sqrt{(k)^{2}+(3)^{2}}$
  
  Squaring on both sides we have,
  
  $(3)^{2}+(k-2)^{2}=(k)^{2}+(3)^{2}$
  
  $9+k^{2}+4-4 k=k^{2}+9$
  
  $4 k=4$
  
  $k=1$
  
  Hence the value of ‘k’ for which the point ‘P’ is equidistant from the other two given points is.