Question

Find the distance between (-1,6) and (5,-2) round your answer to the nearest hundredth if necessary

Answer 1

To find the distance between the points \((-1, 6)\) and \( (5, -2)\), we can use the distance formula:

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

Where:
- \( (x_1, y_1) = (-1, 6) \)
- \( (x_2, y_2) = (5, -2) \)

Substituting the coordinates into the formula:

\[
d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2}
\]

Calculating the differences:

\[
d = \sqrt{(5 + 1)^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

Thus, the distance between the points \((-1, 6)\) and \( (5, -2)\) is **10**. Since this is already an integer, no rounding is necessary.