apply the pythagorean theorem to find the length between the two points (5,5) (2, -3). round your answer to the nearest hundredth if necessary
To find the distance between two points using the Pythagorean theorem, we need to find the lengths of the horizontal and vertical sides of the right triangle formed by the two points.
The horizontal side can be found by subtracting the x-coordinates of the two points: 5 - 2 = 3.
The vertical side can be found by subtracting the y-coordinates of the two points: 5 - (-3) = 8.
Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two points.
Applying the Pythagorean theorem:
distance^2 = horizontal side^2 + vertical side^2
distance^2 = 3^2 + 8^2
distance^2 = 9 + 64
distance^2 = 73
To find the distance, we need to take the square root of both sides of the equation:
distance = sqrt(73)
Rounding to the nearest hundredth, the length between the two points (5,5) and (2,-3) is approximately 8.54.
To find the length between two points using the Pythagorean theorem, follow these steps:
1. Identify the coordinates of the two points: (x₁, y₁) and (x₂, y₂).
In this case, the coordinates are:
Point 1: (5, 5)
Point 2: (2, -3)
2. Calculate the difference between the x-coordinates: (x₂ - x₁).
In this case, the difference is:
2 - 5 = -3
3. Calculate the difference between the y-coordinates: (y₂ - y₁).
In this case, the difference is:
-3 - 5 = -8
4. Square the difference between the x-coordinates: (-3)² = 9.
5. Square the difference between the y-coordinates: (-8)² = 64.
6. Add the squares from steps 4 and 5 together: 9 + 64 = 73.
7. Take the square root of the sum from step 6 to find the length between the points:
√73 ≈ 8.54 (rounded to the nearest hundredth).
Therefore, the length between the points (5, 5) and (2, -3) is approximately 8.54 (rounded to the nearest hundredth).
To apply the Pythagorean theorem to find the distance between two points in a coordinate plane, you can follow these steps:
1. Identify the coordinates of the two points. In this case, the first point is (5, 5) and the second point is (2, -3).
2. Find the difference between the x-coordinates and the y-coordinates of the two points. For the x-coordinates, subtract the x-coordinate of the second point from the x-coordinate of the first point. For the y-coordinates, subtract the y-coordinate of the second point from the y-coordinate of the first point.
Δx = 2 - 5 = -3
Δy = -3 - 5 = -8
3. Square the differences obtained in step 2. Square Δx and square Δy.
(Δx)^2 = (-3)^2 = 9
(Δy)^2 = (-8)^2 = 64
4. Add the squares obtained in step 3.
(Δx)^2 + (Δy)^2 = 9 + 64 = 73
5. Take the square root of the sum obtained in step 4 to find the distance between the two points.
distance = √73
6. Round the distance to the nearest hundredth, if necessary. In this case, the distance is already in the square root form, so we don't need to round it.
Therefore, the length between the two points (5, 5) and (2, -3) is approximately √73.