Find area of the triangle with vertices at the point given in each of the following:
(i) \((1,0), (6,0), (4,3)\)
(ii) \((2,7), (1,1), (10,8)\)
(iii) \((-2,-3), (3,2), (-1,-8)\)
(i) \(\frac{15}{2}\)
(ii) \(\frac{47}{2}\)
(iii) 15
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 4 sq. units and vertices are
(i) \((k,0), (4,0), (0,2)\)
(ii) \((-2,0), (0,4), (0,k)\)
(i) \(k = 0,\; 8\)
(ii) \(k = 0,\; 8\)
(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.
(i) \(y = 2x\)
(ii) \(x - 3y = 0\)
If area of triangle is 35 sq units with vertices \((2,-6), (5,4)\) and \((k,4)\). Then \(k\) is
(A) 12
(B) -2
(C) -12, -2
(D) 12, -2
(D)