P ( x, y ) be any point on AB. Then, area of triangle ABP is zero (Why?). So = This gives ( ) y – x = or y = x , which is the equation of required line AB. Also, since the area of the triangle ABD is sq.
units, we have k = ± This gives, k = ± , i.e., k = ∓ . EXERCISE . . Find area of the triangle with vertices at the point given in each of the following : (i) ( , ), ( , ), ( , ) (ii) ( , ), ( , ), ( , ) (iii) (– , – ), ( , ), (– , – ) .
Show that points A ( a, b + c ), B ( b, c + a ), C ( c, a + b ) are collinear. . Find values of k if area of triangle is sq. units and vertices are (i) ( k , ), ( , ), ( , ) (ii) (– , ), ( , ), ( , k ) .
(i) Find equation of line joining ( , ) and ( , ) using determinants. (ii) Find equation of line joining ( , ) and ( , ) using determinants. . If area of triangle is sq units with vertices ( , – ), ( , ) and ( k , ).
Then k is (A) (B) – (C) – , – (D) , – . Minors and Cofactors In this section, we will learn to write the expansion of a determinant in compact form using minors and cofactors. Definition Minor of an element a ij of a determinant is the determinant obtained by deleting its i th row and j th column in which element a ij lies. Minor of an element a ij is denoted by M ij .
Remark Minor of an element of a determinant of order n ( n ≥ ) is a determinant of order n – . Example Find the minor of element in the determinant ∆= Solution Since lies in the second