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
4
4
8
8
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To apply the Pythagorean Theorem, we need to find the lengths of the sides of the rectangle.
The length of side AB is 3-1 = 2 and the length of side BC is 4-2 = 2. Since these two sides are parallel, we can see that opposite sides of the rectangle are congruent.
Using the Pythagorean Theorem, we can find the length of the diagonal of the square. The diagonal is the hypotenuse of a right triangle with sides AB and BC.
Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the sides and c is the length of the hypotenuse, we can calculate:
2^2 + 2^2 = c^2
4 + 4 = c^2
8 = c^2
Taking the square root of both sides, we find:
c = √8
c ≈ 2.83
Therefore, the length of the diagonal of the square is approximately 2.83.