The points A(x,2), B(­2,1) and C(6,­3) are collinear. Find x?

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 $$\triangle$$ 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)