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
2.65
2.65
29
29
5.38
5.38
4.58
To apply the Pythagorean Theorem, we need to find the length of the hypotenuse of a right triangle formed by connecting the points (2, 5) and (7, 3).
The length of the horizontal side of the triangle is the difference between the x-coordinates of the two points:
7 - 2 = 5.
The length of the vertical side of the triangle is the difference between the y-coordinates of the two points:
3 - 5 = -2.
To find the length of the hypotenuse, we square the length of the horizontal side and the length of the vertical side, and then take the square root of their sums:
hypotenuse length = sqrt((5^2) + (-2)^2)
hypotenuse length = sqrt(25 + 4)
hypotenuse length = sqrt(29)
Rounding to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.38.
Therefore, the correct answer is:
5.38
To apply the Pythagorean Theorem, we need to find the length of the hypotenuse of a right triangle. The two given points (2, 5) and (7, 3) can be used to form the legs of the triangle.
First, we need to find the length of the horizontal leg. This can be done by subtracting the x-coordinates of the two points:
7 - 2 = 5
Next, we need to find the length of the vertical leg. This can be done by subtracting the y-coordinates of the two points:
3 - 5 = -2
Since we need the length, we take the absolute value of the vertical leg:
|-2| = 2
Now, we can use the Pythagorean Theorem to find the length of the hypotenuse. The formula is:
c = sqrt(a^2 + b^2)
Where c is the length of the hypotenuse, and a and b are the lengths of the legs.
Substituting in the values we found:
c = sqrt(5^2 + 2^2)
= sqrt(25 + 4)
= sqrt(29)
Rounding to the nearest hundredth, we get:
c ≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39.
To apply the Pythagorean theorem to find the length between two points in a coordinate plane, you need to follow these steps:
Step 1: Identify the coordinates of the two points.
In this case, the coordinates are:
Point A: (2, 5)
Point B: (7, 3)
Step 2: Find the horizontal distance (difference in x-coordinates) between the two points.
In this case, the horizontal distance is: 7 - 2 = 5
Step 3: Find the vertical distance (difference in y-coordinates) between the two points.
In this case, the vertical distance is: 3 - 5 = -2
Step 4: Square both the horizontal distance and the vertical distance.
Horizontal distance squared: 5^2 = 25
Vertical distance squared: (-2)^2 = 4
Step 5: Add the two squared distances together.
25 + 4 = 29
Step 6: Take the square root of the sum to find the length between the two points.
√29 = 5.385164807134504
Step 7: Round the answer to the nearest hundredth, if necessary. In this case, round 5.385164807134504 to the nearest hundredth: 5.38.
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.38.