Apply the Pythagorean theorem to find the length between (2,5) and (7,3) round to the nearest hundredth if necessary.
To apply the Pythagorean theorem, we need to calculate the distance between the two points using their coordinates.
Let's label the points:
Point A: (2, 5)
Point B: (7, 3)
The distance between these two points can be found using the following formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Substituting the coordinates of the points:
Distance = √((7 - 2)² + (3 - 5)²)
Distance = √(5² + (-2)²)
Distance = √(25 + 4)
Distance = √29
Rounding to the nearest hundredth, the distance between (2, 5) and (7, 3) is approximately 5.39.
To find the length between the two points (2,5) and (7,3) using the Pythagorean theorem, follow these steps:
Step 1: Identify the coordinates of the two points:
Point A: (2,5)
Point B: (7,3)
Step 2: Find the difference in the x-coordinates (Δx) and the difference in the y-coordinates (Δy):
Δx = x2 - x1 = 7 - 2 = 5
Δy = y2 - y1 = 3 - 5 = -2
Step 3: Square the differences:
Δx^2 = 5^2 = 25
Δy^2 = (-2)^2 = 4
Step 4: Apply the Pythagorean theorem:
The length between the two points is given by:
Length = √(Δx^2 + Δy^2)
Substituting the values:
Length = √(25 + 4)
Length = √29
Length ≈ 5.39 (rounded to the nearest hundredth)
Therefore, the length between (2,5) and (7,3), rounded to the nearest hundredth, is approximately 5.39 units.
To apply the Pythagorean theorem in this case, we need to find the distance between two points in a coordinate plane. Here's how you can do it step by step:
1. Determine the coordinates of the two points:
- Point 1: (2, 5)
- Point 2: (7, 3)
2. Identify the differences in the x-coordinates and the y-coordinates:
- Δx = x2 - x1 = 7 - 2 = 5
- Δy = y2 - y1 = 3 - 5 = -2
3. Use the Pythagorean theorem formula to find the distance between the two points:
- Distance = √(Δx² + Δy²)
Plugging in the values:
- Distance = √(5² + (-2)²)
- Distance = √(25 + 4)
- Distance = √29
4. Round the distance to the nearest hundredth:
- Distance ≈ 5.39 (rounded to two decimal places)
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.39 units.