Question

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear. [2 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark

A (1 , -1) , B (5 , 2) and C (9 , 5) are the given points. Then, We have
Distance between the points is given by
$\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$
$AB=\sqrt{{(5-1)}^2+{(2+1)}^2}$
So,

$AB=\sqrt{16+9}=5$

$BC=\sqrt{{(5-9)}^2+{(2-5)}^2}$

$BC=\sqrt{16+9}=5$

and , $AC=\sqrt{{(1-9)}^2+{(-1-5)}^2}$

$AC=\sqrt{64+36}=10$

Clearly, AC = AB + BC

Hence A, B, C are collinear points