The line y = 3x - 2 bisects the join of (a, 3) and (2, -5), find the value of a.

By mid-point formula,

Mid-point of (a, 3) and (2, -5) = $\dfrac{a + 2}{2}, \dfrac{3 + (-5)}{2}$

= $\dfrac{a + 2}{2}, \dfrac{-2}{2}$

= $\Big(\dfrac{a + 2}{2}, -1\Big)$.

Given, line y = 3x - 2 bisects the join of (a, 3) and (2, -5).

∴ $\Big(\dfrac{a + 2}{2}, -1\Big)$ satisfies the equation y = 3x - 2.

$\therefore -1 = 3 \times \dfrac{a + 2}{2} - 2 \\[1em] \Rightarrow -1 = \dfrac{3a + 6}{2} - 2 \\[1em] \Rightarrow -1 = \dfrac{3a + 6 - 4}{2} \\[1em] \Rightarrow -2 = 3a + 2 \\[1em] \Rightarrow 3a = -4 \\[1em] \Rightarrow a = -\dfrac{4}{3}.$

Hence, a = $-\dfrac{4}{3}$.