Question

Find the distance between the points (
–
7,0) and (
–
3,
–
9).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units

Answer 1

To find the distance between the points \((-7, 0)\) and \((-3, -9)\), we can use the distance formula, which is given by:

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

Here, we have the points \((x_1, y_1) = (-7, 0)\) and \((x_2, y_2) = (-3, -9)\).

Substituting the coordinates into the distance formula:

\[
d = \sqrt{((-3) - (-7))^2 + ((-9) - 0)^2}
\]

Now, let's simplify each part:

1. Calculate \((-3) - (-7)\):
\[
-3 + 7 = 4
\]

2. Calculate \((-9) - 0\):
\[
-9 - 0 = -9
\]

Now plug these values back into the formula:

\[
d = \sqrt{(4)^2 + (-9)^2}
\]

Calculating the squares:

\[
d = \sqrt{16 + 81}
\]

Adding those together gives:

\[
d = \sqrt{97}
\]

Thus, the distance between the points \((-7, 0)\) and \((-3, -9)\) is:

\[
\sqrt{97} \text{ units}
\]