Question

Calculate the distance between the points C= (3, - 8) and E= (7, - 1) In the coordinate plane.
Give an exact answer (not a decimal approximation) -

Answer 1

To calculate the distance between the points \( C(3, -8) \) and \( E(7, -1) \) in the coordinate plane, we use the distance formula:

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

Here, \( (x_1, y_1) = (3, -8) \) and \( (x_2, y_2) = (7, -1) \).

1. Calculate \( x_2 - x_1 \):

\[
x_2 - x_1 = 7 - 3 = 4
\]

2. Calculate \( y_2 - y_1 \):

\[
y_2 - y_1 = -1 - (-8) = -1 + 8 = 7
\]

3. Now substitute these values back into the distance formula:

\[
d = \sqrt{(4)^2 + (7)^2}
\]

4. Calculate the squares:

\[
4^2 = 16 \quad \text{and} \quad 7^2 = 49
\]

5. Add the squares:

\[
16 + 49 = 65
\]

6. Take the square root:

\[
d = \sqrt{65}
\]

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

\[
\sqrt{65}
\]