Question

Apply the Pythagorean
Theorem to find the length
between and .
Round your answer to the
nearest hundredth, if
necessary. (1 point)
(2, 5) (7, 3)
29
2.65
4.58
5.39

Answer 1

To find the length between the points \((2, 5)\) and \((7, 3)\), 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 \((2, 5)\) and \((7, 3)\):

- \(x_1 = 2\)
- \(y_1 = 5\)
- \(x_2 = 7\)
- \(y_2 = 3\)

Substituting these values into the distance formula gives:

\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]

Calculating inside the square root:

1. Calculate \(7 - 2 = 5\)
2. Calculate \(3 - 5 = -2\)

Now plug those into the formula:

\[
d = \sqrt{(5)^2 + (-2)^2}
\]

Calculating the squares:

- \(5^2 = 25\)
- \((-2)^2 = 4\)

Summing those results:

\[
d = \sqrt{25 + 4} = \sqrt{29}
\]

Now, calculating \(\sqrt{29}\):

\(\sqrt{29} \approx 5.385\)

Rounded to the nearest hundredth, the distance is:

\[
d \approx 5.39
\]

Thus, the length between the points \((2, 5)\) and \((7, 3)\) is approximately **5.39**.