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

(i) Slope of AB$=\frac{12-8}{5-4}=\frac{4}{1}=4$

Slope of BC$=\frac{28-12}{9-5}=\frac{16}{4}=4$

Hence AB$||$BC, but B is a point of intersect.

Hence A, B, C are collinear.

(ii) Slope of AB$=\frac{-6+18}{3-16}=\frac{12}{-13}=-\frac{12}{13}$

Slope of BC$=\frac{6+6}{-10-3}=\frac{12}{-13}=-\frac{12}{13}$

Slope of AB$=$ slope of BC

Hence A, B, C are collinear.