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.
explanation: The document contains a math question and its corresponding solution. The question asks for the value of \( k \) such that the point \( P(0, 2) \) is equidistant from the points \( (3, k) \) and \( (k, 5) \). The solution is provided, and it concludes that \( k = 1 \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding solution. The question asks for the value of \( k \) such that the point \( P(0, 2) \) is equidistant from the points \( (3, k) \) and \( (k, 5) \). The solution is provided, and it concludes that \( k = 1 \).
  
  Label: question-and-answer