If a square A B C D , where A(0,0), B(2,0), C(2,2) and D(0,2) undergoes the following transformations successively, then the final figure would be a (i) f₁(x, y) (y, x) (ii) f₂(x, y) (x+3 y, y) (iii) f₃(x, y) ( x-y 2 , x+y 2 )

Step-by-step solution

Given, square A B C D when A(0,0), B(2,0), C(2,2) , D(0,2) undergoes the following transformations. (i) f₁(x, y) (y, x) (ii) f₂(x, y) (x+3 y, y) (iii) f₃(x, y) ( x-y 2 , x+y 2 ) By the transformation f₁(x, y) (y, x) , we get aligned & A(0,0) A(0,0) & B(2,0) B(0,2) & C(2,2) C(2,2) and D(0,2) D(2,0) aligned Now, perform f₂(x, y) (x+3 y, y) So, A(0,0) A(0,0), B(0,2) B(6,2) aligned & C(2,2) C(8,2), D(2,0) D(2,0) & Next perform f₃(x, y) ( x-y 2 , x+y 2 ) aligned aligned & A(0,0) A(0,0), B(6,2) B(2,4) & C(8,2) C(3,5), D(