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

2.65
2.65

5.38
5.38

4.58

Answer 1

To find the distance between two points using the Pythagorean Theorem, we need to find the length of the legs of a right triangle formed by the points.

The given points are (2, 5) and (7, 3).

The length of the horizontal leg is the difference in x-coordinates:
7 - 2 = 5

The length of the vertical leg is the difference in y-coordinates:
3 - 5 = -2

We can use these leg lengths to find the hypotenuse (distance) using the Pythagorean Theorem:
distance = sqrt(5^2 + (-2)^2)

distance = sqrt(25 + 4)

distance = sqrt(29)

Rounding to the nearest hundredth, the distance is approximately 5.39.

Therefore, the correct response is: 5.38.