Use the Pythagorean theorem to find the side length of square (-7,6) (-2,-6) (10,-1) (5,11) in feet
To find the side length of the square, we need to calculate the distance between any two opposite corners of the square.
Using the Pythagorean theorem, the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the distance between the points (-7, 6) and (10, -1):
Distance = √((10 - (-7))² + (-1 - 6)²)
= √(17² + (-7)²)
= √(289 + 49)
= √338
≈ 18.39 feet
Therefore, the side length of the square is approximately 18.39 feet.
To find the side length of the square using the Pythagorean theorem, we need to calculate the distance between two opposite vertices of the square.
Let's label the four given points as follows:
A: (-7, 6)
B: (-2, -6)
C: (10, -1)
D: (5, 11)
We can calculate the distance between points A and B using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates, we get:
AB = √[(-2 - (-7))^2 + (-6 - 6)^2]
Simplifying further:
AB = √[(5)^2 + (-12)^2]
AB = √[25 + 144]
AB = √169
AB = 13 feet
Hence, the side length of the square is 13 feet.
To find the side length of a square using the Pythagorean theorem, we need to calculate the distance between two opposite corners of the square. Given the coordinates of the four corners (-7, 6), (-2, -6), (10, -1), and (5, 11), we can use these points to find the distance between two opposite corners.
Let's take the points (-7, 6) and (10, -1) as our two opposite corners. We can calculate the distance between these two points using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the triangle represent the horizontal and vertical distances between the points. Let's call the horizontal distance x and the vertical distance y.
The horizontal distance (x) is the difference between the x-coordinates of the two points:
x = 10 - (-7) = 10 + 7 = 17.
The vertical distance (y) is the difference between the y-coordinates of the two points:
y = -1 - 6 = -7.
Now, we can use these values to calculate the distance (d) using the Pythagorean theorem:
d = sqrt(x^2 + y^2).
Plugging in the values, we get:
d = sqrt(17^2 + (-7)^2).
Calculating further:
d = sqrt(289 + 49).
d = sqrt(338).
d ≈ 18.384.
Therefore, the side length of the square is approximately 18.384 feet.