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 ABCD. If A B=√ 10 and the points A and C lie on the…

Let $\displaystyle \alpha, \beta, \gamma, \delta \in \mathbb{Z}$ and let $\displaystyle A(\alpha, \beta), B(1,0), C(\gamma, \delta)$ and $\displaystyle D(1,2)$ be the vertices of a parallelogram ABCD . If $\displaystyle A B=\sqrt{10}$ and the points A and C lie on the line $\displaystyle 3 y=2 x+1$, then $\displaystyle 2(\alpha+\beta+\gamma+\delta)$ is equal to