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Question

Prove that the area of triangle with vertices (t,t2),(t+2,t+2),(t+3,t) is independent of t.

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Solution

Area of Triangle with vertices A(t,t2),B(t+2,t+2),C(t+3,t)

AreaofABC=∣ ∣ ∣ ∣tt2t+2t+2t+3ttt2∣ ∣ ∣ ∣=12|t2+2tt2+4+t2+2tt25t6+t2+t6t2|=12|8|=4
(is independent of t)

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