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
5.39
5.39
2.65
2.65
4.58
4.58
To find the length between two points using the Pythagorean Theorem, we need to find the length of the two sides of a right triangle formed by the two points.
The coordinates of the first point are (2, 5), and the coordinates of the second point are (7, 3).
The vertical distance between the two points can be calculated by taking the absolute difference of the y-coordinates: |5 - 3| = 2.
The horizontal distance between the two points can be calculated by taking the absolute difference of the x-coordinates: |2 - 7| = 5.
Now we can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Using the vertical and horizontal distances we found, the hypotenuse length (the distance between the two points) can be calculated as:
√(2^2 + 5^2) = √(4 + 25) = √29 ≈ 5.39
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.39.
So the correct response is:
5.39