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 calculate the difference in the x-coordinates (horizontal distance) and the difference in the y-coordinates (vertical distance).
Let's label the coordinates as follows:
Point 1: (x1, y1) = (2, 5)
Point 2: (x2, y2) = (7, 3)
The horizontal distance (dx) is given by:
dx = x2 - x1 = 7 - 2 = 5
The vertical distance (dy) is given by:
dy = y2 - y1 = 3 - 5 = -2
Now, we can use the Pythagorean theorem to find the length (d) between the two points:
d = √(dx² + dy²)
= √(5² + (-2)²)
= √(25 + 4)
= √29
Rounded to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.39.
To apply the Pythagorean Theorem, follow these steps:
1. Identify the coordinates of the two points:
Point 1: (2, 5)
Point 2: (7, 3)
2. Calculate the difference in x-coordinates (Δx):
Δx = x-coordinate of Point 2 - x-coordinate of Point 1
= 7 - 2
= 5
3. Calculate the difference in y-coordinates (Δy):
Δy = y-coordinate of Point 2 - y-coordinate of Point 1
= 3 - 5
= -2
4. Use the Pythagorean Theorem formula to find the length between the points:
Length = √(Δx^2 + Δy^2)
= √((5)^2 + (-2)^2)
= √(25 + 4)
= √29
≈ 5.39
Therefore, the length between the points (2, 5) and (7, 3) is approximately 5.39 units.
To apply the Pythagorean Theorem to find the length between two points, we need to calculate the distance between those points in a coordinate plane using the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's consider the given points (2, 5) and (7, 3) as (x1, y1) and (x2, y2) respectively.
So, for these points, we have:
x1 = 2, y1 = 5
x2 = 7, y2 = 3
Now, let's substitute these values into the formula and solve the equation to find the distance (d):
d = √((7 - 2)^2 + (3 - 5)^2)
Simplifying the equation, we get:
d = √(5^2 + (-2)^2)
d = √(25 + 4)
d = √29
Therefore, the length between the points (2, 5) and (7, 3) is √29, which is approximately 5.39 when rounded to the nearest hundredth.