Q12 of 23 Page 330

If the three points (a, 0), (0, b) and (1, 1) are collinear then let us show that

Let the collinear points be


A = (x1, y1) = (a, 0) and


B = (x2, y2) = (0, b) and


C = (x3, y3) = (1, 1)


The area of triangle formed by joining points A, B and C will be 0 because A, B and C are collinear


Area of triangle is given by


Area = × [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]


Where (x1, y1), (x2, y2) and (x3, y3) are vertices of triangle


⇒ 0 = × [a(b – 1) + 0(1 – 0) + 1(0 – b)]


⇒ 0 = ab – a + (-b)


⇒ a + b = ab


Divide throughout by ab


⇒ + =


⇒ + = 1


Hence proved


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