Question

The vertices of a rectangle are (1, 1), (8, 1), (8,4), and (1, 4). What is the length of its diagonals?

A. 7
B. 3
C. sq root 40
D. sq root 58

Answer 1

The length of the diagonals of the rectangle is sqrt(58).

Step-by-step explanation:

To find the length of the diagonals of a rectangle, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can calculate the length of the two diagonals of the rectangle:

Diagonal 1 = sqrt((8 - 1)^2 + (4 - 1)^2) = sqrt(7^2 + 3^2) = sqrt(49 + 9) = sqrt(58)

Diagonal 2 = sqrt((8 - 1)^2 + (1 - 4)^2) = sqrt(7^2 + (-3)^2) = sqrt(49 + 9) = sqrt(58)

Therefore, the length of the diagonals of the rectangle is sqrt(58).