Question

.verify that the point(1,5)(2,3)(-2,-1)arecollinear or not

Answer 1

Three points (x1,y1) , (x2,y2) , (x3 , y3) are collinear if the area of triangle formed by them is zero.

If u have bit of knowledge of co-ordinate geometry

U must be knowing that the area of triangle formed by (x1,y1),(x2,y2),(x3,y3) is given by 1/2*[x1(y2-y3) + x2 (y3 - y1) + x3 ( y1-y2)]

SO, finding the area formed by the 3 points , A = (1/2)*[1(3-(-1)) + 2(-1 - 5) -2 (5-3)]

A = (1/2) * [ 4 -12 -4] 
It is clearly not equal to  zero

so , the three points are not collinear.

Hope , this helps !

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