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) $
The final figure will be
Options:
A) A square
B) A rhombus
C) A rectangle
D) A parallelogram
Show Answer
Answer:
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.
BETA
