Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

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.

Answer 3

[AI-generated answer — Explain Bot]

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.