Answer the following questions related to collinearity of three points in the plane.
a. (a) State the algebraic condition involving the coordinates of points X(x1,y1), Y(x2,y2) and Z(x3,y3) that guarantees the three points are collinear.
b. (b) Explain, without performing numerical calculation, why the condition stated in part (a) implies that the area of triangle XYZ is zero, and hence X, Y and Z lie on the same straight line.