Question

Are the given points collinear?
The points are (1, – 1), (5, 2) and (9, 5).

• A. Yes
• B. No
• C. Maybe

Answer 1

The correct option is A Yes

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

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

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

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

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

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

Clearly, AC = AB + BC

Hence A, B, C are collinear points