A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 5. Data points marked are point A at (1,2), point B at (3, 2), point C at (3, 4), and point D at (1, 4). A line joins points A to B, B to C, C to D, and D to A, forming a rectangle.
Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
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, we are looking for the diagonal of the rectangle which forms the square.
The length of one side of the square can be found by calculating the distance between points A and B, which is 3 - 1 = 2 units.
Using the Pythagorean Theorem, let's calculate the length of the diagonal.
Diagonal^2 = side1^2 + side2^2
Diagonal^2 = 2^2 + 2^2
Diagonal^2 = 4 + 4
Diagonal^2 = 8
To find the length of the diagonal, we take the square root of 8:
Diagonal ≈ √8 ≈ 2.83
Therefore, the length of the diagonal of the square is approximately 2.83 units.