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

29
29

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 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 \( (x_2, y_2) = (7, 3) \).

1. Calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):

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

2. Substitute into the distance formula:

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

3. Calculate \( \sqrt{29} \):

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

Rounding to the nearest hundredth, we get:

\[ d \approx 5.39 \]

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