Answer :

If Three points (a,b), (c,d), (e,f) are collinear then the area formed by the triangle by the three points is zero.

Area of a triangle = ...(1)


1.
(a,b) = (1,-3)


(c,d) = (2,-5)


(e,f) = (-4,7)


Area =


Area = = 0


Hence the points are collinear.


2.
(a,b) = (-2,3)


(c,d) = (1,-3)


(e,f) = (5,4)


Area =


Area =


Hence the points are not collinear.


3.
(a,b) = (0,3)


(c,d) = (2,1)


(e,f) = (3,-1)


Area =


Area =


Hence the points are non collinear.


4.
(a,b) = (-2,3)


(c,d) = (1,2)


(e,f) = (4,1)


Area =


Area =


Hence the points are collinear.

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