Question

(7,8)
(3,2)

Apply the Pythagorean theorem to find the length between the two points. Round your answer to the nearest hundredth.

Answer 1

15 16

Find the slant height of the square pyramid.

Answer 2

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

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

For the points \((7, 8)\) and \((3, 2)\), we have:

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

Now we will substitute these values into the distance formula:

\[
d = \sqrt{(3 - 7)^2 + (2 - 8)^2}
\]

Calculating the differences:

\[
d = \sqrt{(-4)^2 + (-6)^2}
\]

Calculating the squares:

\[
d = \sqrt{16 + 36}
\]

Adding the results:

\[
d = \sqrt{52}
\]

Now, we can simplify \(\sqrt{52}\):

\[
d = \sqrt{4 \cdot 13} = 2\sqrt{13}
\]

Now, we calculate \(2\sqrt{13}\):

Using a calculator, we find:

\[
\sqrt{13} \approx 3.60555
\]

So:

\[
2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111
\]

Now we round this to the nearest hundredth:

\[
d \approx 7.21
\]

Therefore, the distance between the two points \((7, 8)\) and \((3, 2)\) is approximately \(7.21\) units.