| i. \[{{f}_{1}}(x,y)\to (y,x)\] |
| ii. \[{{f}_{2}}(x,y)\to (x+3y,y)\] |
| iii. \[{{f}_{3}}(x,y)\to ((x-y)/2,(x+y)/2)\] |
A) A square
B) A rhombus
C) A rectangle
D) A parallelogram
Correct Answer: D
Solution :
[d] Clearly, A will remain as (0,0); \[{{f}_{1}}\] will make B as \[(0,4),{{f}_{2}}\] will make it \[(12,4)\] and \[{{f}_{3}}\] will make it \[(4,8);{{f}_{1}}\] will make C as \[(2,4){{f}_{2}}\] will make it \[(14,4)\] and \[{{f}_{3}}\] will make it (5, 9) finally, \[{{f}_{1}}\] will make D as \[(2,0){{f}_{2}}\] will make it (2, 0) and \[{{f}_{3}}\] will make it (1, 1). So, we finally get A(0, 0), B(4, 8), C(5, 9), and \[D(1,1).\] Hence, \[{{m}_{AB}}=\frac{8}{4},\,\,{{m}_{BC}}=\frac{9-8}{5-4}=1,\,\,{{m}_{CD}}=\frac{9-1}{5-1}=\frac{8}{4},\] \[{{m}_{AD}}=1,\,\,{{m}_{AC}}=\frac{9}{5},\,\,{{m}_{BD}}=\frac{8-1}{4-1}=\frac{7}{3}\] Hence, the final figure will be a parallelogram.
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