Chapter 1.2, Problem 83E

Proof Prove that if the points $(x_1,y_1)$ and $(x_2,y_2)$ lie on the same line as $(x_1^{*},y_1^{*})$ and $(x_2^{*},y_2^{*})$ then

$\frac{y_2^{*}-y_1^{*}}{x_2^{*}-x_1^{*}}=\frac{y_2-y_1}{x_2-x_1}.$

Assume $x_1\ne x_2$ and $x_1^{*}\ne x_2^{*}$