Use the image to answer the question.
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 left parenthesis 1 comma 2 right parenthesis, point B at left parenthesis 3 comma 2 right parenthesis, point C at left parenthesis 3 comma 4 right parenthesis, and point D at left parenthesis 1 comma 4 right parenthesis. 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.
(1 point)
Responses
2.83
2.83
4.24
4.24
8
8
4
4
To find the length of the diagonal of the rectangle, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the rectangle are the length and the width, and the diagonal is the hypotenuse.
Using the points given, we can calculate the length and width of the rectangle:
Length = x-coordinate of point C - x-coordinate of point A = 3 - 1 = 2
Width = y-coordinate of point C - y-coordinate of point A = 4 - 2 = 2
Now, we can find the length of the diagonal using the Pythagorean Theorem:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 2^2 + 2^2
Diagonal^2 = 4 + 4
Diagonal^2 = 8
Taking the square root of both sides:
Diagonal = √8
Rounding to the nearest hundredth:
Diagonal ≈ 2.83
Therefore, the length of the diagonal of the square is approximately 2.83.