Question

Find the distance using the distance formula
(-4,5)(0,-6)

Answer 1

To find the distance between the two points \((-4, 5)\) and \((0, -6)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-4, 5)\) and \((x_2, y_2) = (0, -6)\).

Now, substitute the coordinates into the formula:

\[
d = \sqrt{(0 - (-4))^2 + (-6 - 5)^2}
\]

This simplifies to:

\[
d = \sqrt{(0 + 4)^2 + (-6 - 5)^2}
\]
\[
d = \sqrt{(4)^2 + (-11)^2}
\]
\[
d = \sqrt{16 + 121}
\]
\[
d = \sqrt{137}
\]

Thus, the distance between the points \((-4, 5)\) and \((0, -6)\) is \(\sqrt{137}\).