Ex 4.3,1 (i) - Chapter 4 Class 12 Determinants (Term 1)

Transcript

Ex 4.3,1 Find area of the triangle with vertices at the point given in each of the following: • (1, 0), (6, 0), (4, 3) The area of triangle is given by ∆ = 1﷮2﷯ x1﷮y1﷮1﷮x2﷮y2﷮1﷮x3﷮y3﷮1﷯﷯ Here, x1 = 1 , y1 = 0 x2 = 6 ,y2 = 0 x3 = 4 ,y3 = 3 ∆ = 1﷮2﷯ 1﷮0﷮1﷮6﷮0﷮1﷮4﷮3﷮1﷯﷯ = 1﷮2﷯ 1 0﷮1﷮3﷮1﷯﷯−0 6﷮1﷮4﷮1﷯﷯+1 6﷮0﷮4﷮3﷯﷯﷯ = 1﷮2﷯ (1(0 – 3) – 0(6 – 4) + 1 (18 – 0)) = 1﷮2﷯ (1( – 3) + 0 + 1 (18) ) = 1﷮2﷯ [ – 3 + 18 ] = 15﷮2﷯ Thus, the required area of triangle is 𝟏𝟓﷮𝟐﷯ square units