# 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.
The text contains a mathematical question and its solution, where the goal is to find the value of 'k' for a point P to be equidistant from two other points.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.
user
The text contains a mathematical question and its solution, where the goal is to find the value of 'k' for a point P to be equidistant from two other points.

TYPE: SINGLE_QUESTION_WITH_ANSWER