Question

What is the distance between points j and k if j is at (-3, 2) and k is at (1, -6)

Answer 1

To find the distance between two points \( j (-3, 2) \) and \( k (1, -6) \), we can use the distance formula:

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

Where:
- \( (x_1, y_1) \) are the coordinates of point \( j \),
- \( (x_2, y_2) \) are the coordinates of point \( k \).

Plugging in the values:

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

Now substituting these into the formula:

\[
d = \sqrt{(1 - (-3))^2 + (-6 - 2)^2}
\]

Simplifying the expressions inside the parentheses:

\[
d = \sqrt{(1 + 3)^2 + (-6 - 2)^2}
\]

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

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

\[
d = \sqrt{80}
\]

We can simplify \( \sqrt{80} \):

\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\]

Thus, the distance between points \( j \) and \( k \) is:

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