Question

Find the distance between the points (
–
4,
–
7) and (
–
10,
–
10).
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 \((-4, -7)\) and \((-10, -10)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-4, -7)\) and \((x_2, y_2) = (-10, -10)\). Now, we can plug in the values:

1. Calculate \(x_2 - x_1\):

\[
x_2 - x_1 = -10 - (-4) = -10 + 4 = -6
\]

2. Calculate \(y_2 - y_1\):

\[
y_2 - y_1 = -10 - (-7) = -10 + 7 = -3
\]

3. Now substitute these values into the distance formula:

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

4. Calculate \((-6)^2\) and \((-3)^2\):

\[
(-6)^2 = 36
\]
\[
(-3)^2 = 9
\]

5. Now add these results together:

\[
d = \sqrt{36 + 9} = \sqrt{45}
\]

6. Finally, simplify \(\sqrt{45}\):

\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

Thus, the distance between the points \((-4, -7)\) and \((-10, -10)\) is

\[
\boxed{3\sqrt{5}}
\]