Prove that the area of a triangle with vertices (t, t-2),(t+2, t+2) and (t+3) is independent of t.
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error in ur question.......
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There is a mistake in the question
It should be Prove that the area of a triangle with vertices (t, t-2),(t+2, t+2) and (t+3 , t) is independent of t.
Area of triangle = 1/2 × | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= 1/2 × | t((t + 2) - t) + (t + 2)(t - (t - 2)) + (t + 3)((t - 2) - (t + 2)) |
= 1/2 × | t(2) + (t +2)(2) + (t + 3)(-4)|
= 1/2 × | 2t + 2t + 4 - 4t - 12 |
= 1/2 × | 4t - 4t + 4 - 12 |
= 1/2 × | -8 |
= 1/2 × 8
= 4 unit square
Hence proved that it is independent of "t"
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