To find the length of the diagonal of the square formed by the points A, B, C, and D, we can use the coordinates provided.
The points are:
- A (1, 2)
- B (3, 2)
- C (3, 4)
- D (1, 4)
It looks like we have a square with two sides along the x-axis and y-axis. The length of one side of the square can be calculated by the distance between points A and B, or D and C.
Calculating the length of side AB (or CD):
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The distance between A(1, 2) and B(3, 2):
\[ \text{Length of AB} = |3 - 1| = 2 \]
Now, to find the diagonal of the square, we can apply the Pythagorean theorem. In a square, the diagonal \(d\) can be calculated using the formula: \[ d = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2} \] where \(s\) is the length of the side of the square.
Substituting \(s = 2\): \[ d = 2\sqrt{2} \]
Calculating \(2\sqrt{2}\): \[ \sqrt{2} \approx 1.414 \] \[ d \approx 2 \times 1.414 = 2.828 \]
Rounding to the nearest hundredth gives: \[ d \approx 2.83 \]
Thus, the length of the diagonal of the square is 2.83.