Question:

Stepwise Solution:

Midpoint of diagonal $AC = \left(\dfrac{-5 + (-1)}{2}, \dfrac{7 + (-6)}{2}\right) = \left(\dfrac{-6}{2}, \dfrac{1}{2}\right) = \left(-3, \dfrac{1}{2}\right)$. [1.0 Mark]

Midpoint of diagonal $BD = \left(\dfrac{-4 + 4}{2}, \dfrac{-5 + 5}{2}\right) = (0, 0)$. [1.0 Mark]

Since the midpoints of diagonals $AC$ and $BD$ do not coincide $\left(\left(-3, \dfrac{1}{2}\right)
eq (0, 0)\right)$, the diagonals do not bisect each other. Hence, $ABCD$ is NOT a parallelogram. [1.0 Mark]

Marking Scheme:

• Calculating midpoint of $AC = (-3, 1/2)$: 1.0 Mark
• Calculating midpoint of $BD = (0, 0)$: 1.0 Mark
• Comparing midpoints and concluding NOT a parallelogram: 1.0 Mark