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Question

A rectangle ABCD, where A(0,0),B(4,0),C(4,2),D(0,2), undergoes the following transformation successively :
(i)f1(x,y)(y,x)
(ii)f2(x,y)(x+3y,y)
(iii)f3(x,y)(xy2,x+y2)
Then the final figure is :

A
square
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B
parallelogram
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C
rhombus
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D
rectangle
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Solution

The correct option is B parallelogram
Clearly, A will remain as (0,0);f1 will make B as (0,4),f2 will make it (12,4) and f3 will make it (5,9). Finally, f1 will make D as (2,0),f2 will make it (2,0) and f3 will make if (1,1). So finally we get A(0,0),B(4,8),C(5,9),D(1,1). Therefore,
mAB=84,mBC=9854=1
mCD=9151=84
mAD=1,mAC=95,mBD=8141=73
Hence, the final figure will be parallelogram.

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