Question

Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary. a. (1,2) b. (3,2) c. (3,4) d. (1,4)

a. 4.24
b. 2.83
c. 8
d. 4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the diagonal of a square, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).

Let's use coordinates to find the length of the diagonal of each square:

a. (1,2)
The side length of the square is the distance between the two points (1,2) and (1,0) which is 2 units. So, the diagonal is the hypotenuse of a right triangle with two sides of length 2.
diagonal = sqrt(2^2 + 2^2) = sqrt(8)≈2.83

b. (3,2)
The side length of the square is the distance between the two points (3,2) and (3,0) which is 2 units. So, the diagonal is the hypotenuse of a right triangle with two sides of length 2.
diagonal = sqrt(2^2 + 2^2) = sqrt(8)≈2.83

c. (3,4)
The side length of the square is the distance between the two points (3,4) and (3,0) which is 4 units. So, the diagonal is the hypotenuse of a right triangle with two sides of length 4.
diagonal = sqrt(4^2 + 4^2) = sqrt(32)≈5.66

d. (1,4)
The side length of the square is the distance between the two points (1,4) and (1,0) which is 4 units. So, the diagonal is the hypotenuse of a right triangle with two sides of length 4.
diagonal = sqrt(4^2 + 4^2) = sqrt(32)≈5.66

Therefore, the correct lengths of the diagonals are:
a. 2.83
b. 2.83
c. 5.66
d. 5.66