1. The points A(x,2), B(2,1) and C(6,3) are collinear. Find x?
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By: anil on 05 May 2019 02.15 am
Coordinates of points A(x,2), B(2,1) and C(6,3) 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 => $$frac{1}{2} [x(1-3)+2(3-2)+6(2-1)]=0$$ => $$-2x+2+6=0$$ => $$-2x = -8$$ => $$x = frac{8}{2} = 4$$ => Ans - (C)
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