Question

A rectangle ABCD, A ≡ (0, 0), B ≡ (4, 0), C ≡ (4, 2), 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) $f_3(x,y)\to (\frac{x-y}{2},\frac{x+y}{2})$.
The final figure will be

• A. a square
• B. a rhombus
• C. a rectangle
• D. a parallelogram

Answer 1

The correct option is D a parallelogram

On applying (i), (ii) and (iii) transformation,
we finally get $A\equiv (0,0),B\equiv (4,8),C\equiv (5,9),D\equiv (1,1)$
$m_{AB}=\frac{8}{4},m_{BC}=\frac{9-8}{5-4}=1,m_{CD}=\frac{9-1}{5-1}=\frac{8}{4},m_{AD}=1,m_{AC}=\frac{9}{5},m_{BD}=\frac{8-1}{4-1}=\frac{7}{3}.$
Hence, final figure will be parallelogram.