Question

Find the distance
(-3,-7) (-2,6)

Answer 1

To find the distance between the points \((-3, -7)\) and \((-2, 6)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-3, -7)\) and \((x_2, y_2) = (-2, 6)\).

Now, substituting the values into the formula:

\[
d = \sqrt{((-2) - (-3))^2 + (6 - (-7))^2}
\]

Calculating the differences:

\[
d = \sqrt{(-2 + 3)^2 + (6 + 7)^2}
\]
\[
d = \sqrt{(1)^2 + (13)^2}
\]
\[
d = \sqrt{1 + 169}
\]
\[
d = \sqrt{170}
\]

Thus, the distance between the points \((-3, -7)\) and \((-2, 6)\) is:

\[
d \approx 13.04
\]

So the exact distance is \(\sqrt{170}\) or approximately \(13.04\).