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)→(x−y2,x+y2)
The final figure will be
a parallelogram
A remains (0, 0)
f1(B)=(0,4), f2(f1(B))=(12,4), and f3(f2(f1(B)))=(12−42,12+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 =9−15−1=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.