Apply the Pythagorean Theorem to find the length between (2,5) and (7,3). Round your answer to the nearest hundredth, if necessary.
1. 2.65
2. 29
3. 4.58
4. 5.38
To apply the Pythagorean Theorem, we need to find the distance between the points (2,5) and (7,3).
First, we can find the horizontal distance between the two points by subtracting the x-coordinates:
7 - 2 = 5
Then, we can find the vertical distance between the two points by subtracting the y-coordinates:
3 - 5 = -2
Next, we can use these distances to form a right triangle. The horizontal distance (5) and vertical distance (-2) will be the legs of the triangle.
Using the Pythagorean Theorem, we can find the length of the hypotenuse (d), which is the distance between the two points:
d^2 = (5)^2 + (-2)^2
d^2 = 25 + 4
d^2 = 29
Taking the square root of both sides, we find:
d = √29 ≈ 5.39
Therefore, the length between (2,5) and (7,3) is approximately 5.39.
Rounding this to the nearest hundredth, the answer is 5.38.
So the correct answer is 4. 5.38.
To apply the Pythagorean Theorem to find the length between two points (x1, y1) and (x2, y2), we can use the following formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point are (2,5) and the coordinates of the second point are (7,3). Plug these values into the formula:
Distance = √((7 - 2)^2 + (3 - 5)^2)
Distance = √((5)^2 + (-2)^2)
Distance = √(25 + 4)
Distance = √29
Rounding to the nearest hundredth, the answer is 5.39. So, the correct option is 4. 5.38.