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Question

A rectangle ABCD, A = (0,0), B = (4, 0), C = (4, 2), D = (0, 2) undergoes the following transformations successively.
(i) f1(x,y)(y,x)
(ii) f2(x,y)(x+3y,y)
(iii) f3(x,y)(xy2,x+y2)
The final figure will be


A

a square

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B

a rhombus

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C

a rectangle

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D

a parallelogram

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Solution

The correct option is D

a parallelogram


A remains (0, 0)
f1(B)=(0,4), f2(f1(B))=(12,4), and f3(f2(f1(B)))=(1242,12+42)=(4,8)
So finally B = (4, 8)
C=(4,2)f1(2,4)f2(14,4)f3(5,9)D=(0,2)f1(2,0)f2(2,0)f3(1,1)
So Slope of AB =84=2
Slope of CD =9151=2
Slope of BC = 1
Slope of AD = 1
So, AB is parallel to DC, BC is parallel to AD. Length of AB length of BC, AB is not perpendicular to BC.
Hence ABCD is a parallelogram.


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