Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth if necessary. (1,4) (3,4) (3,2) (1,2)
OMG i got 1/5.... so if u dont want to make that same mistake here:
1. 2.83
2. 5.39
3. 10
4. 6:40
5. 8.54
bye! :3
To find the length of the diagonal of the square, we need to find the distance between two opposite corners of the square. Let's use the Pythagorean theorem:
Let's consider two opposite corners of the square, namely (1,4) and (3,2).
The vertical distance between these two points is the difference between their y-coordinates: 4 - 2 = 2.
The horizontal distance between these two points is the difference between their x-coordinates: 3 - 1 = 2.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
Diagonal^2 = vertical distance^2 + horizontal distance^2
Diagonal^2 = 2^2 + 2^2
Diagonal^2 = 4 + 4
Diagonal^2 = 8
Taking the square root of both sides, we get:
Diagonal = √8 ≈ 2.83
Rounding to the nearest hundredth, the length of the diagonal of the square is approximately 2.83.
To apply the Pythagorean Theorem and find the length of the diagonal of the square, we need to first understand the theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a square with coordinates (1,4), (3,4), (3,2), and (1,2). Each side of the square is a right triangle. We can choose any two adjacent points to form a right triangle.
Let's choose the points (1,4) and (3,4) to form a right triangle. The horizontal distance between these two points is 2 units, and the vertical distance is 0 units. This means that the hypotenuse of this right triangle is the diagonal of the square.
Applying the Pythagorean Theorem to this right triangle, we can calculate the length of the diagonal as follows:
Hypotenuse squared = (Horizontal distance)^2 + (Vertical distance)^2
Hypotenuse squared = 2^2 + 0^2
Hypotenuse squared = 4
To find the length of the hypotenuse (diagonal), we take the square root of both sides of the equation:
Hypotenuse = √4
Hypotenuse = 2
Therefore, the length of the diagonal of the square is 2 units.
To find the length of the diagonal of the square, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonal of the square forms the hypotenuse, and the sides of the square form the other two sides of the right triangle.
Let's label the coordinates of the four vertices of the square as A(1, 4), B(3, 4), C(3, 2), and D(1, 2).
To find the length of the diagonal, we'll first find the length of one side of the square and then use it to find the length of the diagonal.
First, we'll find the length of side AB using the distance formula:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((3 - 1)^2 + (4 - 4)^2)
= sqrt(2^2 + 0^2)
= sqrt(4)
= 2
Now that we have the length of one side, we can use it to find the length of the diagonal. Since it's a square, all sides are equal in length.
Using the Pythagorean Theorem, the length of the diagonal (AC) is:
AC^2 = AB^2 + BC^2
AC^2 = 2^2 + 2^2
AC^2 = 4 + 4
AC^2 = 8
To find the actual length of the diagonal, we take the square root of both sides:
AC = sqrt(8)
AC ≈ 2.83 (rounded to the nearest hundredth)
Therefore, the length of the diagonal of the square is approximately 2.83 units.