Distance and the Pythagorean Theorem Quick Check
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Question
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
4
8
8
4.24
4.24
The length of the diagonal of the square can be found by using the Pythagorean Theorem.
The length of one side of the square can be found by finding the distance between points A and B. This distance is √((3-1)^2 + (2-2)^2) = √2.
Since the square is a rectangle, the diagonal will be the hypotenuse of a right triangle with sides √2 and √2.
Using the Pythagorean Theorem, the length of the diagonal is √(2^2 + 2^2) = √8 = 2.83 (rounded to the nearest hundredth).
Therefore, the answer is 2.83.