Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) Round your answer to the nearest hundredth, if necessa
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The formula for the distance between two points in a coordinate plane is given by the Pythagorean Theorem:
√((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point (x1, y1) are (2, 5) and the coordinates of the second point (x2, y2) are (7, 3).
Using the formula, we can substitute the values:
√((7 - 2)^2 + (3 - 5)^2)
Simplifying further:
√(5^2 + (-2)^2)
√(25 + 4)
√29
Hence, the length between the two points is approximately 5.39, rounded to the nearest hundredth.
To find the distance between two points using the Pythagorean Theorem, you can follow these steps:
Step 1: Identify the coordinates of the two points. In this case, the coordinates are (2, 5) and (7, 3).
Step 2: Calculate the difference in the x-coordinates and the difference in the y-coordinates.
Δx = 7 - 2 = 5
Δy = 3 - 5 = -2
Step 3: Use the Pythagorean Theorem formula to find the distance.
Distance = √(Δx^2 + Δy^2)
Plugging in the calculated values:
Distance = √(5^2 + (-2)^2)
= √(25 + 4)
= √29
≈ 5.39 (rounded to the nearest hundredth)
Therefore, the distance between the points (2, 5) and (7, 3) is approximately 5.39.
To apply the Pythagorean theorem to find the length between two points (x1, y1) and (x2, y2), you need to follow these steps:
Step 1: Identify the coordinates of the two points. In this case, the coordinates are (2, 5) and (7, 3).
Step 2: Determine the difference between the x-coordinates and y-coordinates of the two points. Subtract the x-coordinate of the first point from the x-coordinate of the second point, and then subtract the y-coordinate of the first point from the y-coordinate of the second point. In this case:
x2 - x1 = 7 - 2 = 5
y2 - y1 = 3 - 5 = -2
Step 3: Square the differences from step 2. Square the difference in x-coordinates (5^2) and the difference in y-coordinates (-2^2):
(x2 - x1)^2 = 5^2 = 25
(y2 - y1)^2 = (-2)^2 = 4
Step 4: Add the squares from step 3. Add the squares of the differences:
(x2 - x1)^2 + (y2 - y1)^2 = 25 + 4 = 29
Step 5: Take the square root of the sum from step 4. Take the square root of 29:
√29 ≈ 5.39
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.39.