(1,4) (3,4) (1,2) (3,2) find the diagonal of the square. Round the answer to nearest hundredth If necessarily
To find the diagonal of a square, we can use the distance formula between two points.
Let's label the given points as A(1,4), B(3,4), C(1,2), and D(3,2).
The diagonal of a square connects opposite vertices. In this case, it connects points A and C, or points B and D.
Using the distance formula, the distance between A(1,4) and C(1,2) is:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
d = √[(1 - 1)^2 + (2 - 4)^2]
d = √[0^2 + (-2)^2]
d = √[0 + 4]
d = √4
d = 2
Therefore, the length of the diagonal of the square is 2.
To find the diagonal of a square, we can use the distance formula between two points.
Let's calculate the distance between the points (1,4) and (3,4) first:
Distance = √((x2 - x1)² + (y2 - y1)²)
= √((3 - 1)² + (4 - 4)²)
= √(2² + 0²)
= √(4)
= 2
Now, let's calculate the distance between the points (1,2) and (3,2):
Distance = √((x2 - x1)² + (y2 - y1)²)
= √((3 - 1)² + (2 - 2)²)
= √(2² + 0²)
= √(4)
= 2
Since the diagonal passes through these two points, the length of the diagonal of the square is twice the distance we just calculated, which is 2 + 2 = 4.
Therefore, the diagonal of the square is 4 (rounded to the nearest hundredth).
To find the length of the diagonal of a square, you can use the distance formula. The distance formula calculates the length between two points (x1, y1) and (x2, y2) in the Cartesian coordinate system.
For this problem, we have four points: (1,4), (3,4), (1,2), and (3,2). Let's label them as point A (1,4), point B (3,4), point C (1,2), and point D (3,2).
To calculate the diagonal, we need to find the length between either of the two opposite vertices. In this case, we can find the distance between point A and point C (the length of one side of the square) and then multiply it by the square root of 2 to get the length of the diagonal.
Calculating the distance between A and C:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((1 - 1)^2 + (2 - 4)^2)
Distance = √(0^2 + (-2)^2)
Distance = √(0 + 4)
Distance = √4
Distance = 2
Now, to find the length of the diagonal, we multiply the length of one side by the square root of 2:
Diagonal = 2 * √2
Rounding to the nearest hundredth, the diagonal of the square is approximately 2.83.