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
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)))=(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.