Question

Find the distance between the points (–4, 5) and (–9, –1).
Write your answer as a whole number or a fully simplified radical expression. Do not round.

Answer 1

To find the distance between the points \((-4, 5)\) and \((-9, -1)\), we can use the distance formula given by:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

Assign the points as follows:
- \(x_1 = -4\), \(y_1 = 5\)
- \(x_2 = -9\), \(y_2 = -1\)

Now, we calculate the differences:
\[
x_2 - x_1 = -9 - (-4) = -9 + 4 = -5
\]
\[
y_2 - y_1 = -1 - 5 = -6
\]

Next, we substitute these values into the distance formula:
\[
d = \sqrt{(-5)^2 + (-6)^2}
\]
\[
d = \sqrt{25 + 36}
\]
\[
d = \sqrt{61}
\]

Thus, the distance between the points \((-4, 5)\) and \((-9, -1)\) is \(\sqrt{61}\). Since \(\sqrt{61}\) is already in its simplest radical form, we conclude:

\[
\boxed{\sqrt{61}}
\]