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
4.24
4.24
8
8
2.83
To find the length of the diagonal of the square, we can use the Pythagorean Theorem, which states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, since the rectangle formed by connecting the points A, B, C, and D is a square, the two sides adjacent to the right angle are equal in length.
The length of one side of the square can be found by subtracting the x-coordinate of point A from the x-coordinate of point B (3 - 1 = 2). And since the sides are equal, the length of the other side is found by subtracting the y-coordinate of point A from the y-coordinate of point D (4 - 2 = 2).
Now, we can apply the Pythagorean Theorem to find the length of the diagonal:
Diagonal^2 = Side^2 + Side^2
Diagonal^2 = 2^2 + 2^2
Diagonal^2 = 4 + 4
Diagonal^2 = 8
To find the length of the diagonal, we need to take the square root of both sides:
Diagonal = √8
Rounded to the nearest hundredth, the length of the diagonal is approximately 2.83.
Therefore, the correct answer is 2.83.