question_answer

Area of the triangle with vertices (a, b),\[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}}),\] where \[a,\,{{x}_{1}}\] and \[{{x}_{2}},\] are in G.P. with common ratio r and b, \[{{y}_{1}}\] and \[{{y}_{2}}\] are in G.P. with common ratio s, is given by

A)  \[ab\,(r-1)\,\,(s-1)\,\,(s-r)\]

B)  \[\frac{1}{2}\,\,ab\,(r+1)\,\,(s+1)\,\,(s-r)\]

C)  \[\frac{1}{2}\,\,ab\,(r-1)\,\,(s-1)\,\,(s-r)\]

D)  \[ab\,(r+1)\,\,(s+1)\,\,(r-s)\]

E)  None of these.