Question

Calculate the distance between the points P= (2, 0) and E= (-2, 3) in the coordinate plane.
Give an exact answer (not a decimal approximation).

Answer 1

To calculate the distance between the points \( P(2, 0) \) and \( E(-2, 3) \) in the coordinate plane, we can use the distance formula:

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

Here, we identify the coordinates of the points:
- \( P = (x_1, y_1) = (2, 0) \)
- \( E = (x_2, y_2) = (-2, 3) \)

Now, we plug the coordinates into the distance formula:

\[
d = \sqrt{((-2) - 2)^2 + (3 - 0)^2}
\]

Calculating the differences:

\[
-2 - 2 = -4 \quad \text{and} \quad 3 - 0 = 3
\]

Substituting these differences back into the formula:

\[
d = \sqrt{(-4)^2 + (3)^2}
\]

Calculating the squares:

\[
d = \sqrt{16 + 9}
\]

Now, adding the values inside the square root:

\[
d = \sqrt{25}
\]

Finally, taking the square root gives:

\[
d = 5
\]

Thus, the exact distance between the points \( P \) and \( E \) is \( \boxed{5} \).