­ The points A(3,­2), B(1,4) and C(­2,x) are collinear. What is the value of x?

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 $$\triangle$$ 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)