Question

Calculate the distance between the points K = (-8, -2) and G = (-2, 4) in the coordinate plane.

Answer 1

To calculate the distance between the points \( K = (-8, -2) \) and \( G = (-2, 4) \) in the coordinate plane, we use the distance formula:

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

Where:
- \( (x_1, y_1) = (-8, -2) \)
- \( (x_2, y_2) = (-2, 4) \)

Substituting the coordinates into the formula:

1. Calculate \( x_2 - x_1 \):

\[
x_2 - x_1 = -2 - (-8) = -2 + 8 = 6
\]

2. Calculate \( y_2 - y_1 \):

\[
y_2 - y_1 = 4 - (-2) = 4 + 2 = 6
\]

3. Now plug these values into the distance formula:

\[
d = \sqrt{(6)^2 + (6)^2} = \sqrt{36 + 36} = \sqrt{72}
\]

4. Simplifying \( \sqrt{72} \):

\[
\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
\]

So, the distance \( d \) between the points \( K \) and \( G \) is

\[
\boxed{6\sqrt{2}}
\]