Ex 4.2,1 (ii) - Chapter 4 Class 12 Determinants

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Ex 4.2, 1 Find area of the triangle with vertices at the point given in each of the following: (ii) (2, 7), (1, 1), (10, 8) The area of triangle is given by ∆ = 1/2 |■8(x1&y1&1@x2&y2&1@x3&y3&1)| Here, x1 = 2 , y1 = 7 x2 = 1 , y2 = 1 x3 = 10 , y3 = 8 ∆ = 1/2 |■8(2&7&1@1&1&1@10&8&1)| = 1/2 (2|■8(1&1@8&1)|−7|■8(1&1@10&1)|+1|■8(1&1@10&8)|) = 1/2 ( 2(1 – 8) – 7(1 – 10) + 1 (8 – 10) ) = 1/2 (2(–7) – 7(–9) + 1 (–2) ) = 1/2 ( – 14 + 63 – 2 ) = 1/2 [– 16 + 63] = 47/2 Thus, the required area of triangle is 𝟒𝟕/𝟐 square units