Question

Prove that by adding the points (2,0), (5,0), (6,2), and (3,2) one after the other, a parallelogram is formed. ​

Answer 1

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 !!!!!!