Question

Using the method of slope, show that the following points are collinear :

$\left(i\right)A(4,8),B(5,12),C(9,28)\left(ii\right)A(16,-18),B(3,-6),C(-10,6)$

Answer 1

$\left(i\right)A(4,8),B(5,12),C(9,28)\text{Slope of}AB=\frac{y_2-y_1}{x_2-x_1}=\frac{12-8}{5-4}=\frac{4}{1}=4\text{Slope}BC=\frac{y_2-y_1}{x_2-x_1}=\frac{28-12}{9-5}=\frac{16}{4}=4\text{Since slope of AB = Slope of BC}\text{Slope of}CA=\frac{8-28}{4-9}=\frac{-20}{-5}=4\text{Since all 3 line segments have the same slope, they are parallel.}\text{Since they have a common point B, they are collinear.}\left(ii\right)A(16,-18),B(3,-6),C(-10,6)\text{Slope of}AB=\frac{y_2-y_1}{x_2-x_1}=\frac{-6-(-18)}{3-16}=\frac{12}{-13}\text{Slope of}BC=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-6)}{-10-3}=\frac{12}{-13}\text{Slope of}CA=\frac{6-(-18)}{-10-6}=\frac{12}{-13}\text{Since all 3 line segments have the same slope and share a common vertex B, they are collinear.}$