Question

Plot the following point and check whether they are collinear or not:-
(i) (-1,0),(0,1),(2,3)
(ii) (1,1),(2,-3),(-1,-2)​

Answer 1

Answer:

I) (-1,0),(0,1),(2,3).

x₁=−1,x₂=0,x₃=2

y₁=0,y₂=1,y₃=3

collinear formula=

1/2(x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)=0

1/2(-1(1-3)+0(3-0)+2(0-1)=0

1/2(-1(-2)+0+(-2)=0

2+0-2=0

0=0

there fore it is a collinear.

(ii) (1,1),(2,-3),(-1,-2)

x₁=1,x₂=2,x₃=-1

y₁=1,y₂=-3,y₃=-2

collinear formula=

1/2(x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)=0

1/2(1(-3-(-2)+2(-2-1)+-1(1-(-3)=0

1/2(1(-1)+2(-3)+-1(4)=0

1/2(-1-6-4)=0

-11≠0

so its is not a collinear.