Points A(-5, x), B(y, 7) and C(1, -3) are collinear (i.e. lie on same straight line) such that AB = BC. Calculate the values of x and y.

Since, A, B and C are collinear and AB = BC.

We can say that B is the mid-point of AC.

By formula,

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

Substituting value we get,

$\Rightarrow B = \Big(\dfrac{-5 + 1}{2}, \dfrac{x + (-3)}{2}\Big) \\[1em] \Rightarrow (y, 7) = \Big(\dfrac{-4}{2}, \dfrac{x - 3}{2}\Big) \\[1em] \Rightarrow y = \dfrac{-4}{2} \text{ and } 7 = \dfrac{x - 3}{2} \\[1em] \Rightarrow y = -2 \text{ and } x - 3 = 14 \\[1em] \Rightarrow y = -2 \text{ and } x = 17.$

Hence, x = 17 and y = -2.