Question

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) $f_3(x,y)\to \left(\frac{x-y}{2},\frac{x+y}{2}\right)$
then the final figure is?

• A. Square
• B. Parallelogram
• C. Rhombus
• D. Rectangle

Answer 1

The correct option is A Square

Given the sides of a square ABCD i.e, A(0,0) ; B(2,0) ;C(2,2) and D(0,2)

When the transformation take place.

i) $f_1(x,y)\to (y,x)$

$\therefore A(0,0),B(0,2)C(2,2)andD(2,0)$

ii) $f_2(x,y)\to (x+3y,y)$

$A(0,0),B(6,2),C(8,2)andD(2,0)$

Applying the third set of changes on the vertices

$A(0,0),B(2,4),C(0,4),D(2,0)$

$\therefore$ By joining there,we would get a square.