Question

Apply the Pythagorean Theorem to find the length between (2, 5)
and (7, 3)
. Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the distance between the points \((2, 5)\) and \((7, 3)\) using the Pythagorean Theorem, we can follow these steps:

1. First, determine the differences in the \(x\) and \(y\) coordinates:
\[
\Delta x = x_2 - x_1 = 7 - 2 = 5
\]
\[
\Delta y = y_2 - y_1 = 3 - 5 = -2
\]

2. Now, use the distance formula, which is derived from the Pythagorean Theorem:
\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\]
Plugging in the values we found:
\[
d = \sqrt{(5)^2 + (-2)^2}
\]

3. Calculate the squares:
\[
d = \sqrt{25 + 4} = \sqrt{29}
\]

4. Finally, calculate \(\sqrt{29}\) and round to the nearest hundredth:
\[
\sqrt{29} \approx 5.385
\]

Rounded to the nearest hundredth, the length between the points \((2, 5)\) and \((7, 3)\) is approximately:
\[
\boxed{5.39}
\]