Question

Find the distance between ​P(2​,2​) and Upper Q left parenthesis 7 comma 8 right parenthesis.
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Question content area right
Part 1
The distance between P and Q is
  
enter your response here.
​(Simplify your answer. Type an exact answer using radicals as​ needed.)

Answer 1

To find the distance between the points \( P(2, 2) \) and \( Q(7, 8) \), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (2, 2)\) and \((x_2, y_2) = (7, 8)\).

Now, substituting the coordinates into the formula:

\[
d = \sqrt{(7 - 2)^2 + (8 - 2)^2}
\]

Calculate the differences:

\[
d = \sqrt{(5)^2 + (6)^2}
\]

Now, square the differences:

\[
d = \sqrt{25 + 36}
\]

Add the squared values:

\[
d = \sqrt{61}
\]

Thus, the distance between points \( P \) and \( Q \) is

\[
\sqrt{61}
\]