Question

What is the distance between points J and K if J is at (-3, 2) ad K is at (1, -6)

Answer 1

To find the distance between two points \( J(-3, 2) \) and \( K(1, -6) \) in a 2D coordinate plane, we can use the distance formula:

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

Here, \( (x_1, y_1) \) are the coordinates of point \( J \) and \( (x_2, y_2) \) are the coordinates of point \( K \).

Plugging in the values:

- \( x_1 = -3 \)
- \( y_1 = 2 \)
- \( x_2 = 1 \)
- \( y_2 = -6 \)

Now we calculate:

1. Calculate \( x_2 - x_1 \):

\[
x_2 - x_1 = 1 - (-3) = 1 + 3 = 4
\]

2. Calculate \( y_2 - y_1 \):

\[
y_2 - y_1 = -6 - 2 = -8
\]

3. Apply the distance formula:

\[
d = \sqrt{(4)^2 + (-8)^2}
\]

Calculating the squares:

\[
d = \sqrt{16 + 64} = \sqrt{80}
\]

Simplifying \( \sqrt{80} \):

\[
d = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5}
\]

Thus, the distance between points \( J \) and \( K \) is:

\[
\boxed{4\sqrt{5}}
\]