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
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.
To find the length between two points using the Pythagorean Theorem, you need to calculate the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates of the two points.
Given the points (2, 5) and (7, 3), let's calculate the length between them:
Step 1: Find the difference in the x-coordinates:
7 - 2 = 5
Step 2: Find the difference in the y-coordinates:
3 - 5 = -2
Step 3: Square the differences:
5^2 = 25
(-2)^2 = 4
Step 4: Sum the squared differences:
25 + 4 = 29
Step 5: Take the square root of the sum:
√29 ≈ 5.38516
Rounding the answer to the nearest hundredth, we get approximately 5.38.
Therefore, the correct answer is 5.38.
To apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3), follow these steps:
1. Calculate the difference in x-coordinates: 7 - 2 = 5.
2. Calculate the difference in y-coordinates: 3 - 5 = -2.
3. Square the difference in x-coordinates: 5^2 = 25.
4. Square the difference in y-coordinates: (-2)^2 = 4.
5. Add the squared differences in x and y coordinates: 25 + 4 = 29.
6. Take the square root of the sum: √29 ≈ 5.385.
Therefore, the length between (2, 5) and (7, 3) is approximately 5.38 rounded to the nearest hundredth.