Question

Apply the Pythagorean theorem to find the length of the diagonal of the square. D (1,2) C(3,4) A(1,2) B(3,2)

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)

Let's find the distances between points A(1,2) and B(3,2), as well as points A(1,2) and C(3,4).

For A(1,2) and B(3,2):
dAB = √((3 - 1)^2 + (2 - 2)^2)
= √(2^2 + 0)
= √(4)
= 2

For A(1,2) and C(3,4):
dAC = √((3 - 1)^2 + (4 - 2)^2)
= √(2^2 + 2^2)
= √(4 + 4)
= √(8)
= √(2 * 4)
= 2√2

Since ABCD is a square, the diagonals are congruent. Therefore, the length of the diagonal is 2√2.