Question

Using the method of slope, show that the following points are collinear
(i) A (4, 8), B (5, 12), C (9, 28)
(ii) A (16, − 18), B (3, −6), C (−10, 6)

Answer 1

(i) A (4, 8), B (5, 12), C (9, 28)

Slope of AB = $\frac{y_2-y_1}{x_2-x_1}=\frac{12-8}{5-4}=\frac{4}{1}=4$

Slope of BC = $\frac{y_2-y_1}{x_2-x_1}=\frac{28-12}{9-5}=\frac{16}{4}=4$

Since, Slope of AB = Slope of BC = 4

Therefore, the given points are collinear.

(ii) A (16, − 18), B (3, −6), C (−10, 6)

Slope of AB = $\frac{y_2-y_1}{x_2-x_1}=\frac{-6+18}{3-16}=-\frac{12}{13}$

Slope of BC = $\frac{y_2-y_1}{x_2-x_1}=\frac{6+6}{-10-3}=-\frac{12}{13}$

Since, Slope of AB = Slope of BC = $-\frac{12}{13}$

Therefore, the given points are collinear.