Question

Calculate the distance between the points J = (-9, 9) and E = (-2, 1) in the coordinate plane.
Give an exact answer (not a decimal approximation).

Answer 1

To find the distance between two points \( J = (-9, 9) \) and \( E = (-2, 1) \) in the coordinate plane, we can use the distance formula:

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

Here, \( (x_1, y_1) = (-9, 9) \) and \( (x_2, y_2) = (-2, 1) \).

Now, we will calculate the differences:

\[
x_2 - x_1 = -2 - (-9) = -2 + 9 = 7
\]
\[
y_2 - y_1 = 1 - 9 = -8
\]

Now we can plug these values into the distance formula:

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

Calculating the squares:

\[
d = \sqrt{49 + 64}
\]
\[
d = \sqrt{113}
\]

Thus, the exact distance between points \( J \) and \( E \) is

\[
\boxed{\sqrt{113}}.
\]