Let A − 2 , − 1 , B 1 , 0 , C α , β and D γ , δ be the vertices of a parallelogram A B C D . If the point C lies on 2 x − y = 5 and the point D lies on 3 x − 2 y = 6 , then the value of α + β + γ + δ is equal to ______.

Step-by-step solution

Given, A − 2 , − 1 , B 1 , 0 , C α , β and D γ , δ be the vertices of a parallelogram A B C D And the point C lies on 2 x − y = 5 and the point D lies on 3 x − 2 y = 6 , Now, plotting the diagram we get, Now, using the midpoint formula we get, P ≡ α − 2 2 , β − 1 2 ≡ γ + 1 2 , δ 2 Now, on comparing we get, α − 2 2 = γ + 1 2 and β − 1 2 = δ 2 ⇒ α − γ = 3 . . . ( 1 ) , β − δ = 1 . . . ( 2 ) Also, given γ , δ lies on 3 x − 2 y = 6 ⇒ 3 γ − 2 δ = 6 . . . 3 And α , β lies on 2 x − y = 5 ⇒ 2 α − β = 5 . . . ( 4 ) On solvi