Apply the Pythagorean theorem to find the length of the diagonal of the square round your answer to the nearest hundredth d (1,4) c(3,4) a(1,2)b(3,2)
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 (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the line segment connecting points A(1,2) and B(3,2) as the base of the right triangle, and the line segment connecting points C(3,4) and D(1,4) as the height of the right triangle. The diagonal of the square will then be the hypotenuse of this right triangle.
First, let's find the length of the base and height of the right triangle:
Base AB = 3 - 1 = 2 units
Height CD = 4 - 2 = 2 units
Now, we can plug these values into the Pythagorean theorem to find the length of the diagonal:
Diagonal^2 = Base^2 + Height^2
Diagonal^2 = 2^2 + 2^2
Diagonal^2 = 4 + 4
Diagonal^2 = 8
To find the length of the diagonal (d), we take the square root of both sides:
Diagonal = √8
Rounded to the nearest hundredth, the length of the diagonal is approximately 2.83 units.