Question

Calculate the distance between the points C=(2,-1) and N=(7,-7) in the coordinate plane. Give an exact answer not a decimal approximation.

Answer 1

To find the distance between the points \( C = (2, -1) \) and \( N = (7, -7) \) in the coordinate plane, we can use the distance formula:

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

where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points. In this case, we have:

- \( (x_1, y_1) = (2, -1) \)
- \( (x_2, y_2) = (7, -7) \)

Now applying the distance formula:

\[
d = \sqrt{(7 - 2)^2 + (-7 - (-1))^2}
\]

Calculating the differences:

\[
d = \sqrt{(5)^2 + (-7 + 1)^2}
\]
\[
d = \sqrt{(5)^2 + (-6)^2}
\]

Calculating the squares:

\[
d = \sqrt{25 + 36}
\]
\[
d = \sqrt{61}
\]

Thus, the exact distance between the points \( C \) and \( N \) is

\[
\boxed{\sqrt{61}}.
\]