Question

Find the distance between the points (2, -10) and (3, -7).
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 \((2, -10)\) and \((3, -7)\), we can use the distance formula, which is:

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

Here, \((x_1, y_1) = (2, -10)\) and \((x_2, y_2) = (3, -7)\). Let's substitute these values into the formula.

1. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = 3 - 2 = 1
\]

2. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = -7 - (-10) = -7 + 10 = 3
\]

3. Now plug these differences into the distance formula:
\[
d = \sqrt{(1)^2 + (3)^2}
\]

4. Calculate the squares:
\[
(1)^2 = 1
\]
\[
(3)^2 = 9
\]

5. Add the squares:
\[
1 + 9 = 10
\]

6. Finally, take the square root:
\[
d = \sqrt{10}
\]

Thus, the distance between the points \((2, -10)\) and \((3, -7)\) is:

\[
\boxed{\sqrt{10}}
\]