Question

Prove that the points (2, 3), (7, 5), (9, 8), (4, 6) are the vertices of a parallelogram.

Answer 1

Let the points be A (2, 3), B (7, 5), C (9, 8) and D (4, 6).

For the given four points to form a parallelogram, the opposite sides must be parallel, i.e., AB should be parallel to DC and BC should be parallel to AD.

Slope of line AB =

Slope of line DC =

Slope of line BC =

Slope of line AD =

⇒ Slope of line AB = Slope of line DC

Slope of line BC = Slope of line AD

Thus, the given vertices form a parallelogram.