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 = (x_{1}, y_{1}) = (3, 1)

Coordinates of B = (x_{2}, y_{2}) = (12, - 2)

Coordinates of C = (x_{3}, y_{3}) = (0, 2)

Area of ∆ABC = ∆ = 1/2 [x_{1} (y_{2} - y_{3} ) + x_{2} (y_{3} - y_{1} ) + x_{3} (y_{1} - y_{2} )]

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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