Question

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

4.58
4.58

2.65
2.65

5.39
5.39

29
29
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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:

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

Substituting the given points:

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

Now we calculate the differences:

\[
x_2 - x_1 = 7 - 2 = 5
\]

\[
y_2 - y_1 = 3 - 5 = -2
\]

Now, substitute these values into the distance formula:

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

Calculating the squares:

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

Now we need to find the square root of 29. Approximating:

\[
\sqrt{29} \approx 5.385
\]

Rounding to the nearest hundredth, we get:

\[
d \approx 5.39
\]

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