Question

D (1,4)
C (3,4)
B (3,2)
A (1,2)

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)

4.24

2.83

4

8

Answer 1

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):
- 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**.