Question

finding the gradients of the diagonals

click through the slideshow for an explanation.

the diagonals are perpendicular, that is, they intersect at right angles, because the gradients wy and xz multiply to give \\(^{-}1\\).

\\ -\frac{1}{3} \times 3 = ^{-}1 \\

finding the equations of the diagonals

Explanation:

Calculate the gradient of diagonal WY

$$ m_{WY} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{6 - (-3)} = \frac{-3}{9} = -\frac{1}{3} $$

Calculate the gradient of diagonal XZ

$$ m_{XZ} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 4}{0 - 3} = \frac{-9}{-3} = 3 $$

Verify perpendicular relationship

$$ m_{WY} \times m_{XZ} = -\frac{1}{3} \times 3 = -1 $$

Answer:

The gradients of the diagonals are:

• Gradient of \(WY = -\frac{1}{3}\)
• Gradient of \(XZ = 3\)

Since the product of their gradients is \(-1\), the diagonals are perpendicular.