Question

If the square ABCD where A (0,0), B(2,0), C(2,2) and D(0,2) undergoes the following 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$$(\frac{x-y}{2},\frac{x+y}{2})$
then the final figure is a

• A. Square
• B. Parallelogram
• C. rhombus
• D. 2x - y = a

Answer 1

The correct option is B Parallelogram

For A(0,0) $f_1(0,0)\to (0,0)f_2(0,0)\to (0+0,0)f_3(0,0)\to (0,0)FinalimageofAis{A}^{\prime }\equiv (0,0)ForB(2,0)f_1(2,0)\to (0,2)f_2(0,2)\to (0+6,2)f_3(6,2)\to (\frac{6-2}{2},\frac{6+2}{2})FinalimageofBis{B}^{\prime }\equiv (2,4)ForC(2,2)f_1(2,2)\to (2,2)f_2(0,2)\to (2+3\times 2,2)f_3(6,2)\to (\frac{8-2}{2},\frac{8+2}{2})FinalimageofCis{C}^{\prime }\equiv (3,5)$

$ForD(0,2)f_1(0,2)\to (2,0)f_2(2,2)\to (2+3\times 0,2)f_3(6,2)\to (\frac{2-0}{2},\frac{2+0}{2},)FinalimageofDis{D}^{\prime }\equiv (1,1)A^{\prime }\equiv (0,0),B^{\prime }\equiv (2,4),C^{\prime }\equiv (3,5),D^{\prime }\equiv (1,1)$
Which represent a parallelogram?
Hence, (b) is the correct answer