Remarks i Since area is a positive quantity we always take the absolute value of the determinant in 1 ii If area is given use both positive and negative values of the determinant for calculation iii The area of the triangle formed by three collinear points is zero Example 6 Find the area of the triangle whose vertices are 3 8 4 2 and 5 1 Solution The area of triangle is given by 38 A 4 5 This gives 2 1 1 1 3 2 1 8 4 5 1 4 10 61 2 1 3 72 14 Example 7 Find the equation of the line joining A 1 3 and B 0 0 using determinants and find k if D k 0 is a point such that area of triangle ABD is 3sq units Solution Let P x y be any point on AB Then area of triangle ABP is zero Why So 1 0 0 2 1 3 y Rationalised 2023 24 X This gives which is the equation of required line AB Also since the area of the triangle ABD is 3 sq units we 3 1 10 0 13 y 3x 0 or y 3x k 0 0 3k 3 i e k F 2 2 EXERCISE 4 2 DETERMINANTS 83 iii 2 3 3 2 1 8 e reputished 1 Find area of the triangle with vertices at the point given in each of the following i 1 0 6 0 4 3 ii 2 7 1 1 10 8 2 Show that points A a b c B b c a C c a b are collinear 3 Find values of k if area of triangle is 4 sq units and vertices are i k 0 4 0 0 2 ii 2 0 0 4 0 k 4 i Find equation of line joining 1 2 and 3 6 using determinants ii Find equation of line joining 3 1 and 9 3 using determinants 5 If area of triangle is 35 sq units with vertices 2 6 5 4 and k 4 Then k is