Q. 7 B5.0( 1 Vote )

Using distance formula, examine whether the following sets of points are collinear?

(5, 1), (1, - 1), (11, 4)

Answer :

Given points are A(5, 1), B(1, - 1) and C(11, 4).



We need to check whether these points are collinear.


We know that for three points A, B and C to be collinear, the criteria to be satisfied is a linear relationship between AB, BC and AC.


Let us find the distances first,


We know that distance between two points (x1, y1) and (x2, y2) is







AC = 3√5 ..... (1)







AB = 2√5 ..... (2)







BC = 5√5 ..... (3)


From (1), (2), (3) we can see that AB + AC = BC.


The three points are collinear.


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