Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid-point of AB is (2, 3). Find the values of x and y.

By formula,

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

Given, M = (2, 3)

Substituting values in above formula,

$(2, 3) = \Big(\dfrac{3 + x}{2}, \dfrac{5 + y}{2}\Big) \\[1em] \therefore 2 = \dfrac{3 + x}{2} \text{ and } 3 = \dfrac{5 + y}{2} \\[1em] \Rightarrow 4 = 3 + x \text{ and } 6 = 5 + y \\[1em] \Rightarrow x = 1 \text{ and } y = 1.$

Hence, x = 1 and y = 1.