Question

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

answers:

2.65

29

4.58

5.39

Answer 1

you sure thats the answers?

Answer 2

To find the distance between the points (2, 5) and (7, 3) using the Pythagorean Theorem, we can use the distance formula, which is derived from the theorem:

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

Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).

Now, let's calculate:

1. Compute \((x_2 - x_1)\):
\[
x_2 - x_1 = 7 - 2 = 5
\]

2. Compute \((y_2 - y_1)\):
\[
y_2 - y_1 = 3 - 5 = -2
\]

3. Now plug these values into the distance formula:
\[
d = \sqrt{(5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29}
\]

4. Calculate \(\sqrt{29}\):
\[
d \approx 5.385
\]

Rounding to the nearest hundredth, we get:
\[
d \approx 5.39
\]

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