Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.
A. 2.65
B. 4.58
C. 5.38
D. 29
To find the distance between two points using the Pythagorean Theorem, we use the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, (2, 5) is the point (x1, y1) and (7, 3) is the point (x2, y2).
Substituting the values into the formula:
d = √((7 - 2)^2 + (3 - 5)^2)
= √(5^2 + (-2)^2)
= √(25 + 4)
= √29
Rounding to the nearest hundredth, √29 ≈ 5.39.
Therefore, the correct answer is C. 5.38.
To apply the Pythagorean Theorem to find the length between two points, you need to follow these steps:
1. Identify the coordinates of the two points. In this case, the coordinates are (2, 5) and (7, 3).
2. Determine the difference in x-coordinates and y-coordinates between the two points. In this case, the difference in x-coordinates is 7 - 2 = 5, and the difference in y-coordinates is 3 - 5 = -2.
3. Square the difference in x-coordinates and the difference in y-coordinates. In this case, (5)^2 = 25 and (-2)^2 = 4.
4. Add the squared differences together. In this case, 25 + 4 = 29.
5. Take the square root of the sum. In this case, sqrt(29) ≈ 5.39.
Therefore, the length between the two points is approximately 5.39. Rounded to the nearest hundredth, the answer is 5.38, so the correct option is C.
To find the distance between two points using the Pythagorean Theorem, we can first identify the horizontal and vertical distances between the two points.
Let's use the points (2, 5) and (7, 3).
The horizontal distance is the difference of the x-coordinates:
Horizontal distance = 7 - 2 = 5
The vertical distance is the difference of the y-coordinates:
Vertical distance = 3 - 5 = -2
Now, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (the distance between the two points) is equal to the sum of the squares of the other two sides.
To find the distance, we will use the formula:
Distance = √(horizontal distance^2 + vertical distance^2)
Substituting the values, we get:
Distance = √(5^2 + (-2)^2)
Distance = √(25 + 4)
Distance = √29
Distance ≈ 5.39
Rounding the answer to the nearest hundredth, the correct option is C. 5.38.