Collinear points....?

Question

Bah, I have a test tomorrow for Geometry and I kinda sorta didn't pay attention to when the teacher explained this :O. How do you know when points are collinear?

Like:
Which of the following points is not collinear with the other points?

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

@_@ A step by step explaination would be nice >.<........

Answer 1

You're given four points. Call them A, B, C, and D. You're told that three of the four points are colinear. Here's an algorithm that would work every time.

Find the line f(x) between A and B. Find the line g(x) between C and D. Plug C and D into f(x). They will not both satisfy the equation, since not all four points are colinear. If one satisfies the equation, then the other one is the answer. If neither satisfies the equation, then A or B must be the non-colinear point. Plug A and B into g(x) and whichever does not satisfy the equation is your answer.

Let's apply this to our example. The line joining (1,0) and (2,2) is f(x)=2x-2. The line joining (3,3) and (0,-2) is g(x)=x-2. Plugging (3,3) into f(x) we get 3 = 2(3) - 2. That's not true, so we move on. Plugging (0,-2) into f(x) we get -2 = 2(0) - 2. That's true! So (1,0), (2,2), and (0,-2) are colinear. The point not colinear with the others is (3,3).

Answer 2

You can see that (2,2) and (3,3) both lie on the line y=x, so they are collinear.

The points (1,0) and (0,-2) do not satisfy the equation y=x and so are not collinear with (2,2)and (3,3).

Answer 3

Hmm.. nicely 3 factors are collinear in case you could connect them and that they make a without delay line, so possibly you could purely connect them and say they make a line? sorry no remember if it incredibly is not what you're finding for!