Question

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

4
4

8
8

2.83
2.83

4.24

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the diagonal of the square, we can use the Pythagorean Theorem. The Pythagorean Theorem 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 lengths of the other two sides.

In this case, the diagonal of the square forms a right triangle with two sides of equal length. The length of one side is the distance between points A and B, which is 3 - 1 = 2 units. Using the Pythagorean Theorem, we can find the length of the diagonal.

(diagonal)^2 = (side length)^2 + (side length)^2
(diagonal)^2 = 2^2 + 2^2
(diagonal)^2 = 4 + 4
(diagonal)^2 = 8

Taking the square root of both sides, we get:

diagonal ≈ √8 ≈ 2.83

So, the length of the diagonal of the square is approximately 2.83 units. The correct answer choice is:

2.83