Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary

Question

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

Answer 1

To find the length of the diagonal of the square, we can use the distance formula derived from the Pythagorean Theorem. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using points A(1,2) and C(3,4) as the endpoints of the diagonal, we can find the length of the diagonal by plugging in the appropriate coordinates into the distance formula:

d = √((3 - 1)^2 + (4 - 2)^2)
= √(2^2 + 2^2)
= √(4 + 4)
= √8
≈ 2.83

Therefore, the length of the diagonal of the square is approximately 2.83.