Question

If \( A, B, C, D \) is a rectangle with vertices \( A(0, 0), B(8, 0), C(8, 6), D(0, 6) \), then one of the diagonals of the rectangle is:

• A. 12
• B. 10
• C. 14
• D. 16

Hint:

For a rectangle, use the distance formula to find the length of the diagonal by calculating the distance between opposite vertices.

Answer 1

The Correct Option is B

The given rectangle has vertices \( A(0, 0) \), \( B(8, 0) \), \( C(8, 6) \), and \( D(0, 6) \).
To find the length of the diagonal, we use the distance formula between any two opposite vertices of the rectangle.
Let’s calculate the diagonal from \( A(0, 0) \) to \( C(8, 6) \).
The distance formula is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of \( A(0, 0) \) and \( C(8, 6) \): \[ d = \sqrt{(8 - 0)^2 + (6 - 0)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \]
Therefore, the length of the diagonal is 10 units.