If the square ABCD, where `A(0,0),B(2,0)C(2,2) and D(0,2)` undergoes the following three transformations successively
(i) `f_(1)(x,y) to (y,x)`
(ii) `f_(2)(x,y) to (x+3y,y)`
(iii) `f_(3) (x,y) to ((x-y)/2,(x+y)/2)`
then the final figure is a

If the square ABCD where A(0,0), B(2,0), C(2,2), D(0,2) undergoes the following the transformations successively (i) f_(1)(x,y) to f(y,x) (ii) f_(2) (x,y) to f(x + 3y, y) (iii) f_(3) (x,y) to f((x-y)/(2),(x + y)/(2)) then find nature of the final figure of ABCD

A rectangle A B C D , where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) , undergoes the following transformations successively: f_1(x ,y)to(y ,x) f_2(x , y)to(x+3y ,y) f_3(x , y)to((x-y)/2),(x+y)/2) The final figure will be (a) square (b) a rhombus (c) a rectangle (d) a parallelogram

A rectangle ABCD, where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) undergoes the following transformations successively: f_(1)(x,y)rarr(y,x)f_(2)(x,y)rarr(x+3y,y)f_(3)(x,y)rarr((x-y)/2),(x+y)/2) The final f_(3)(x,y)rarr((x-y)/2),(x+y)/2 ) The final figure will be square (b) a rhombus a rectangle (d) a parallelogram

A rectangle A B C D , where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) , undergoes the following transformations successively: f_1(x ,y)vec(y ,x) f_2(x , y)vec(x+3y ,y) f_3(x , y)vec((x-y)//2),(x+y)//2) The final figure will be

A rectangle A B C D , where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) , undergoes the following transformations successively: f_1(x ,y)vec(y ,x) f_2(x , y)vec(x+3y ,y) f_3(x , y)vec((x-y)//2),(x+y)//2) The final figure will be square (b) a rhombus a rectangle (d) a parallelogram

If f (x,y) =e ^(2x+3y) find 3f_(x) (0,0) - 2f_(y) (0,0):