The points A(1, –3), B(2, –2), C(5, 1) are collinear then the harmonic conjugate of B with respect to A, C is

$$\begin{gathered} \text{B divides AC in the ratio }{x}_1-x_{ }=x-x_2 =1:3 \\ Harmonic conjugate of B with respect to A,C is the point which divides AC \\ in the ratio 1:3 externally =\left[\frac{1\left(5\right)-3\left(1\right)}{1-3},\frac{1\left(1\right)-3(-3)}{1-3}\right] \\ =\left[-1,-5\right] \end{gathered}$$