Question

Find the distance
(-1,7)(6,-5)

Answer 1

To find the distance between the points \((-1, 7)\) and \( (6, -5)\), you can use the distance formula:

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

Here, \((x_1, y_1) = (-1, 7)\) and \((x_2, y_2) = (6, -5)\).

Now, plug in the values:

\[
d = \sqrt{(6 - (-1))^2 + (-5 - 7)^2}
\]

Calculating the differences:

\[
d = \sqrt{(6 + 1)^2 + (-5 - 7)^2}
\]
\[
d = \sqrt{(7)^2 + (-12)^2}
\]

Calculate the squares:

\[
d = \sqrt{49 + 144}
\]
\[
d = \sqrt{193}
\]

Thus, the distance between the points \((-1, 7)\) and \( (6, -5)\) is

\[
\sqrt{193}
\]

If you want a decimal approximation, it is approximately \(13.89\).