Question

prove that the point (2,0), (5,0), (6,2) and (3,2) from a parallelogram when they are joined orderly​

Answer 1

Answer:

Step-by-step explanation:

Given :  (2,0), (5,0), (6, 2)  (3,2)

To find :  Parallelogram or not

Solution:

A = ( 2 , 0)

B = ( 5 , 0)

C = ( 6 , 2)

D = ( 3 , 2)

Slope AB  = (0 - 0)/(5 - 2) =  0/3 = 0

Slope of CD =  ( 2 - 2)/(3 - 6) = 0/(-3) = 0

AB ║ CD

Slope of BC  = ( 2 - 0)/(6 - 5) = 2/1 = 2

Slope of AD = ( 2 - 0)/(3 - 2) =2/1 = 2

AD ║ BC

AB = √(5 - 2)² + (0 - 0)² = 3

CD = √(6 - 3)² + (0 - 0)²  = 3

AB = CD

BC = √(6 - 5)² + (2 - 0)²  = √5

AD = √(3 - 2)² + (2 - 0)² = √5

AD = BC

AB ║ CD  , AB = CD

AD ║ BC  , AD = BC

Opposite sides are equal & parallel

Hence Parallelogram