InterviewSolution
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InterviewSolution
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If a = b = c, prove that the points (a, a2), (b,b2),(c, c2) can never be collinear. |
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Answer» Area of the triangle having vertices (x1, y1), (x2, y2) and (x3, y3) is given by Area of △ = \(\frac{1}2[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1-y_2)]\) For points to be collinear, the Area enclosed by them should be equal to 0 ∴ For given points, Area = \(\frac{1}2[a(b^2 - c^2) + b(c^2- a^2) + c(a^2-b^2)]\) Area = \(\frac{1}2\) |(b – c)(a - b)(c – a)| Area ≠ 0 Also it is given that a ≠ b ≠ c, Hence area of triangle made by these points is never zero. Hence given points are never collinear. |
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