1. The points A(3,2), B(1,4) and C(2,x) are collinear. What is the value of x?
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By: anil on 05 May 2019 02.14 am
Coordinates of points A(3,2), B(1,4) and C(2,x) Since the points are collinear , thus the area of triangle formed by these points = 0 Area of triangle formed by points $$(x_1,y_1)$$ , $$(x_2,y_2)$$ and $$(x_3,y_3)$$ is = $$frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$$ => Area of $$ riangle$$ ABC = 0 => $$frac{1}{2} [3(4-x)+1(x-2)+2(2-4)]=0$$ => $$12-3x+x-2-4=0$$ => $$-2x = -6$$ => $$x = frac{-6}{-2} = 3$$ => Ans - (A)
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