Question

Determine whether the given set of points in each case are collinear or not. (i) (7,–2),(5,1),(3,4) (ii) (–2, –8), (2,–3) (6,2) (iii) (a,–2), (a,3), (a,0)









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Answer 1

I think first consider a triangle having the given three points then find the area of the triangle , if it comes 0 then the points are collinear.
let A(7,-2),B(5,1),C(3,4)
therefore usin
1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|
=1/2|7(1-4)+5(4+2)+3(7-1)|
=1/2|7×(-3)+5×6+3×6|
=1/2|-21+30+18|
=1/2|-21+48|
=1/2|27|
=1/2×27
=13.5
Therefore it's not equal to zero and hence these points are not collinear