Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary
A(1,2) B(3,2) C(3,4) D(1,4)
To find the length of the diagonal of the square, we can use the distance formula derived from the Pythagorean Theorem. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using points A(1,2) and C(3,4) as the endpoints of the diagonal, we can find the length of the diagonal by plugging in the appropriate coordinates into the distance formula:
d = √((3 - 1)^2 + (4 - 2)^2)
= √(2^2 + 2^2)
= √(4 + 4)
= √8
≈ 2.83
Therefore, the length of the diagonal of the square is approximately 2.83.
To find the length of the diagonal of the square, we need to calculate the distance between any two opposite vertices using the Pythagorean Theorem.
Let's take two opposite vertices, A(1,2) and C(3,4).
The distance between two points in a 2D plane can be calculated using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Here, (x1, y1) represent the coordinates of point A(1,2), and (x2, y2) represent the coordinates of point C(3,4).
Substituting the values, we get:
d = √[(3 - 1)^2 + (4 - 2)^2]
= √[(2)^2 + (2)^2]
= √[4 + 4]
= √8
To round the answer to the nearest hundredth, we need to find the square root of 8.
sqrt(8) ≈ 2.83
Therefore, the length of the diagonal of the square is approximately 2.83.
To find the length of the diagonal of the square, we need to find the distance between two of its opposite vertices. In this case, let's consider the distance between points A(1,2) and C(3,4).
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.
To apply the Pythagorean Theorem to find the distance between A and C:
1. Find the difference in x-coordinates (3 - 1 = 2).
2. Find the difference in y-coordinates (4 - 2 = 2).
3. Square each difference (2^2 = 4, 2^2 = 4).
4. Add the squares of the differences: 4 + 4 = 8.
5. Take the square root of the sum to get the length of the diagonal: √8 ≈ 2.83.
Therefore, the length of the diagonal of the square is approximately 2.83 units (rounded to the nearest hundredth).