Q. 54.1( 7 Votes )

The points A (3, 1), B (12, - 2) and C (0, 2) cannot be vertices of a triangle.

Answer :

True

Let the coordinates of A = (x1, y1) = (3, 1)


Coordinates of B = (x2, y2) = (12, - 2)


Coordinates of C = (x3, y3) = (0, 2)


Area of ∆ABC = ∆ = 1/2 [x1 (y2 - y3 ) + x2 (y3 - y1 ) + x3 (y1 - y2 )]


Δ= 1/2 [3 - (2 - 2) + 12(2 - 1) + 0{1 - ( - 2)}]


Δ =1/2 [3( - 4) + 12(1) + 0]


Δ =1/2 ( - 12 + 12)=0


Area of ΔABC = 0


Hence, the points A (3, 1), B (12, - 2) and C (0, 2) are collinear.


So, the points A (3, 1), B (12, - 2) and C (0, 2) can’t be the vertices of a triangle.


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