Question

Coordinate A is (1, 2), B is (3, 2), C is (3, 4) and D is (1, 4). Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.

A. 4.24
B. 8
C. 4
D. 2.83

Answer 1

To find the length of the diagonal of the square formed by the points A(1, 2), B(3, 2), C(3, 4), and D(1, 4), we can use the Pythagorean theorem.

First, we can find the lengths of the sides of the square:

- The distance between A(1, 2) and B(3, 2) (horizontal side) is:
\[
\text{Distance} = |x_2 - x_1| = |3 - 1| = 2
\]

- The distance between A(1, 2) and D(1, 4) (vertical side) is:
\[
\text{Distance} = |y_2 - y_1| = |4 - 2| = 2
\]

Both sides of the square have a length of 2.

Now, to find the length of the diagonal (d) of the square, we apply the Pythagorean theorem, which states:
\[
d^2 = a^2 + b^2
\]
where \(a\) and \(b\) are the lengths of the sides of the square.

In this case:
- \(a = 2\)
- \(b = 2\)

Therefore:
\[
d^2 = 2^2 + 2^2 = 4 + 4 = 8
\]
\[
d = \sqrt{8} = 2\sqrt{2} \approx 2 \times 1.414 = 2.828
\]

Rounding this to the nearest hundredth gives:
\[
d \approx 2.83
\]

Thus, the final answer is:

**D. 2.83**