Chapter P.2, Problem 83E

To determine

To prove: If points $\left(x_1,y_1\right),\left(x_2,y_2\right)$ lie on the same line as $\left(x_1^{*},y_1^{*}\right),\left(x_2^{*},y_2^{*}\right)$ then, the following equation satisfy $\frac{y_2^{\ast }-y_1^{\ast }}{x_2^{\ast }-x_1^{\ast }}=\frac{y_2-y_1}{x_2-x_1}$.