Question

Apply Pythagorean theorem to find the length between two points and round to the nearest hundredth
3,2 and 7,8

Answer 1

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

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

Here, the points are \((3, 2)\) and \((7, 8)\):
- \(x_1 = 3\), \(y_1 = 2\)
- \(x_2 = 7\), \(y_2 = 8\)

Now, plug in the values:

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

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

Approximately, \(\sqrt{13} \approx 3.60555\), so:

\[
d \approx 2 \times 3.60555 \approx 7.2111
\]

Finally, rounding to the nearest hundredth:

\[
d \approx 7.21
\]

Thus, the length between the two points (3, 2) and (7, 8) is approximately **7.21**.