Question

Use the image to answer the question.
8-
7-
6-
5-
4-
3-
2-
1-
0+
0
• (7,8).
• (3, 2)
2
3
4
5
6
8
9
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

Answer 1

To find the distance between the two points \((7, 8)\) and \((3, 2)\), we can use the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Here, \((x_1, y_1) = (7, 8)\) and \((x_2, y_2) = (3, 2)\). We can substitute these values into the formula:

1. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = 3 - 7 = -4
\]

2. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = 2 - 8 = -6
\]

3. Now, substitute these differences into the distance formula:
\[
d = \sqrt{(-4)^2 + (-6)^2}
\]

4. Calculate the squares:
\[
d = \sqrt{16 + 36} = \sqrt{52}
\]

5. Now calculate \(\sqrt{52}\):
\[
d \approx 7.2111
\]

Rounding to the nearest hundredth, the distance \(d\) is approximately:

\[
d \approx 7.21
\]

Therefore, the length between the two points is **7.21**.