Prove that by adding the points (2,0), (5,0), (6,2), and (3,2) one after the other, a parallelogram is formed.
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Given points are
- A(2,0)
- B(5,0)
- C(6,2)
- D(3,2)
A quadrilateral is a parallelogram if the opposite sides are equal.
- AB² = (2-5)² + (0-0)² = 9 + 0 = 9 ⇒ AB = ±3
- BC² = (5-6)² + (0-2)² = 1 + 4 = 5 ⇒ BC = √5
- CD² = (6-3)² + (2-2)² = 9 + 0 = 9 ⇒ CD = ±3
- DA² = (3-2)² + (2-0)² = 1 + 4 = 5 ⇒ DA = √5
∴ AB = CD = ±3 & BC = DA = √5
∴ The opposite sides of the quadrilateral ABCD are equal, the four points from a parallelogram.
HENCE PROVED !!!!!!
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