Question

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

29
29

4.58
4.58

2.65
2.65

5.39

Answer 1

To find the distance between the points (2, 5) and (7, 3) using the Pythagorean Theorem, we can apply the distance formula:

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

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

Calculating the differences:

\[
x_2 - x_1 = 7 - 2 = 5
\]
\[
y_2 - y_1 = 3 - 5 = -2
\]

Now, substituting into the distance formula:

\[
d = \sqrt{(5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29}
\]

Calculating the square root of 29:

\[
d \approx 5.385
\]

Rounding to the nearest hundredth:

\[
d \approx 5.39
\]

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