Let α , β , γ , δ ∈ Z and let A α , β , B 1 , 0 , C γ , δ and D 1 , 2 be the vertices of a parallelogram A B C D . If A B = 10 and the points A and C lie on the line 3 y = 2 x + 1 , then 2 α + β + γ + δ is equal to

Step-by-step solution

Plotting the diagram of the given data we get, We know that diagonals of a parallelogram bisect each other. ⇒ Mid-point of A C = Mid-point of B D ⇒ α + γ 2 , β + δ 2 = 1 + 1 2 , 0 + 2 2 ⇒ α + γ 2 , β + δ 2 = 1 , 1 ⇒ α + γ = 2 , β + δ = 2 ⇒ 2 α + γ + β + δ = 8