Question

3,2
7,8
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

7.21
51.98
6.25
62.25

Answer 1

To find the length between the two points (3, 2) and (7, 8) using the Pythagorean Theorem, we can calculate the distance \(d\) using the distance formula:

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

Where:
- \((x_1, y_1) = (3, 2)\)
- \((x_2, y_2) = (7, 8)\)

Substituting the coordinates into the formula:

\[
d = \sqrt{(7 - 3)^2 + (8 - 2)^2}
\]
\[
= \sqrt{(4)^2 + (6)^2}
\]
\[
= \sqrt{16 + 36}
\]
\[
= \sqrt{52}
\]
\[
= 2\sqrt{13}
\]

Now let's calculate \(2\sqrt{13}\):

First, we can find \(\sqrt{13} \approx 3.60555\)

Now we multiply by 2:

\[
2 \cdot 3.60555 \approx 7.2111
\]

Rounding to the nearest hundredth:

\[
d \approx 7.21
\]

The length between the two points is approximately **7.21**.