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
To find the length between two points using the Pythagorean theorem, follow these steps:
1. Determine the difference in x-coordinates: x2 - x1 = 7 - 2 = 5
2. Determine the difference in y-coordinates: y2 - y1 = 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 results from steps 3 and 4: 25 + 4 = 29
6. Take the square root of the sum from step 5: √29 ≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39 units.
To find the length between the points (2, 5) and (7, 3) using the Pythagorean Theorem, follow these steps:
1. Identify the coordinates of the two points: (2, 5) and (7, 3).
2. Calculate the difference between the x-coordinates (Δx) and the difference between the y-coordinates (Δy):
Δx = 7 - 2 = 5
Δy = 3 - 5 = -2
3. Use the Pythagorean theorem formula:
Length = √(Δx^2 + Δy^2)
4. Plug the values of Δx and Δy into the formula:
Length = √(5^2 + (-2)^2)
5. Simplify the equation:
Length = √(25 + 4)
Length = √29
6. Round the value to the nearest hundredth:
Length ≈ 5.39
Thus, the length between the points (2, 5) and (7, 3) is approximately 5.39.
To apply the Pythagorean Theorem, we need to find the distance between two points in a coordinate plane. In this case, we have the coordinates (2, 5) and (7, 3).
Step 1: Find the difference in the x-coordinates and y-coordinates.
- Difference in x-coordinates: 7 - 2 = 5
- Difference in y-coordinates: 3 - 5 = -2 (note that we take the absolute value)
Step 2: Square both differences.
- (Difference in x-coordinates)^2: 5^2 = 25
- (Difference in y-coordinates)^2: (-2)^2 = 4
Step 3: Add the squared differences.
- 25 + 4 = 29
Step 4: Take the square root of the sum.
- √29 ≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39, rounded to the nearest hundredth.