Area of the triangle with vertices `(a, b), (x_1,y_1) and (x_2, y_2)` where `a, x_1,x_2` which in G.P. common ratiorand `b, y_1, y_2`, are in G.P with common ratio s, is

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 which in G.P. common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is

Area of the triangle with vertices (a, b) (x_(1), y_(1)) and (x_(2), y_(2)) , where a, x_(1), x_(2) are in GP. with common ratio r and b, y_(1), y_(2) are in GP. with common ratio s is :

Area of the triangle with vertices (a, b ), (x_(1), y_(1)) and (x_(2), y_(2)) , where a, x_(1), x_(2) are in G.P. with common ratio r and b, y_(1), y_(2) are in G.P. with common ratio s is :

Prove that the area of the triangle with vertices (p,q),(x_(1),y_(1)) and (x_(2),y_(2)) where p,x_(1),x_(2) are in G.P. with common ratio r_(1) and q, y_(1), y_(2) and in G.P with common ratio r_(2) is (1)/(2) pq(r_(1)-1) (r_(2)-1) (r_(2)-r_(1)) sq unit.

The area of the triangle OAB with vertices O(0,0),A(x_(1),y_(1))B(x_(2),y_(2)) is

The area of the triangle OAB with vertices O(0,0),A(x_(1),y_(1))" and B(x_(2),y_(2)) is

A(a, b), B(x_1, y_1) and C(x_2, y_2) are the vertices of a triangle. If a, x_1, x_2 are in GP with common ratio r and b, y_1,y_2 are in GP with common ratio s, then area of triangle ABC is :