The mid-point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Find the values of a and b.

By formula,

Mid-point (M) = $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get,

$\Rightarrow (1, 2a + 1) = \Big(\dfrac{2a + (-2)}{2}, \dfrac{4 + 2b}{2}\Big) \\[1em] \therefore 1 = \dfrac{2a - 2}{2} \text{ and } 2a + 1 = \dfrac{4 + 2b}{2} \\[1em] \Rightarrow 2a - 2 = 2 \text{ and } 4a + 2 = 4 + 2b \\[1em] \Rightarrow 2a = 4 \text{ and } 2b = 4a - 2 \\[1em] \Rightarrow a = 2 \text{ and } 2b = 4(2) - 2 \\[1em] \Rightarrow a = 2 \text{ and } 2b = 6 \\[1em] \Rightarrow a = 2 \text{ and } b = 3.$

Hence, a = 2 and b = 3.