Question

If the points (11, 4), (1, ─1) and (p, 1) are collinear, find the value of p.

Answer 1

Area of a triangle with vertices (x1,y1) ; (x2,y2)  and (x3,y3)  is ∣∣∣∣∣2x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣∣∣∣∣

Since the given points are collinear, they do not form a triangle, which means area of the triangle is Zero. 

Hence, substituting the points (x1,y1)=(5,1) ; (x2,y2)=(1,P)  and (x3,y3)=(4,2) in the area formula, we get ∣∣∣∣∣25(P−2)+1(2−1)+4(1−P)∣∣

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