Let $\alpha, \beta, \gamma, \delta$ be real numbers such that $\alpha^{2} + \beta^{2} + \gamma^{2} \neq 0$ and $\alpha + \gamma = 1$. Suppose the point $(3, 2, -1)$ is the mirror image of the point $(1, 0, -1)$ with respect to the plane $\alpha x + \beta y + \gamma z = \delta$. Then which of the following statements is/are TRUE?
(A) $\alpha + \beta = 2$
(B) $\delta - \gamma = 3$
(C) $\delta + \beta = 4$
(D) $\alpha + \beta + \gamma = \delta$