Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary
To find the length between two points using the Pythagorean Theorem, we need to find the distance between their x-coordinates and the distance between their y-coordinates, and then use these values to calculate the hypotenuse of the right triangle.
The x-coordinate of the first point is 2, and the x-coordinate of the second point is 7. So the distance between their x-coordinates is 7 - 2 = 5.
The y-coordinate of the first point is 5, and the y-coordinate of the second point is 3. So the distance between their y-coordinates is 5 - 3 = 2.
Now we can use the Pythagorean Theorem to find the length between the two points:
length = √(distance x ² + distance y ²)
= √(5² + 2²)
= √(25 + 4)
= √29
≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39.
To find the length between the 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: Determine the horizontal and vertical distances between the points.
Horizontal distance (Δx) = x-coordinate of Point B - x-coordinate of Point A
= 7 - 2
= 5
Vertical distance (Δy) = y-coordinate of Point B - y-coordinate of Point A
= 3 - 5
= -2
Step 3: Use the formula for the length between two points:
Length (d) = √[(Δx)^2 + (Δy)^2]
Substituting the values we found:
Length (d) = √[(5)^2 + (-2)^2]
= √[(25) + (4)]
= √[29]
Step 4: Round the answer to the nearest hundredth:
Length (d) ≈ 5.39
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.39 units, rounded to the nearest hundredth.
To apply the Pythagorean theorem to find the length between two points, we need to use the coordinates of each point and calculate the distance using the formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's plug in the values:
Point 1: (x1, y1) = (2, 5)
Point 2: (x2, y2) = (7, 3)
Now, we can substitute these values into the formula and solve for the distance:
d = √[(7 - 2)^2 + (3 - 5)^2]
= √[5^2 + (-2)^2]
= √[25 + 4]
= √29
Since we need to round our answer to the nearest hundredth, the length between the points (2, 5) and (7, 3) is approximately 5.39 units.