Question

Prove that the points (2, −3), (6, 7), (8, 3), and (4, −7), taken in order, are the vertices of a parallelogram.

Answer 1

Here, let;

• A = (2, −3),
• B = (6, 7),
• C = (8, 3),
• D = (4, −7),

Compute the midpoints of the diagonals AC and BD.

⇒ Midpoint of AC:

= `((2 + 8)/2, (−3 + 3)/2)`

= (5, 0)

⇒ Midpoint of BD:

= `((6 + 4) / 2, (7 + (−7)) / 2)`

= (5, 0)

The diagonals AC and BD have the exact midpoint, so they bisect each other. A quadrilateral whose diagonals bisect each other is a parallelogram. Therefore, the points, taken in order, are the vertices of a parallelogram.