A rectangle ABCD, where 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. $$f3(x$$,$$y)$$→$$((x$$−$$y)/2$$,$$(x+y)/2)The$$ final figure will be

Question

A rectangle ABCD, where 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. $$f3(x$$,$$y)$$→$$((x$$−$$y)/2$$,$$(x+y)/2)The$$ final figure will be

Infinity Learn · Accepted Answer

Clearly, A will remain as (0$$,$$0);$$f1$$ will make B as (0$$,$$4),$$f2$$ will make it (12$$,$$4) , and $$f3$$ will make it (4$$,$$8);$$f1$$ will  make C as (2$$,$$4),$$f2$$ will make it (14$$,$$4) , and $$f3$$ will make it (5$$,$$9) . Finally, $$f1$$ will make D as (2$$,$$0),$$f2$$ will make it (2$$,$$0) , and $$f3$$ will make it (1$$,$$1) . So, we finally get A≡(0$$,$$0),B≡(4$$,$$8),C≡(5$$,$$9) , and D≡(1$$,$$1) . Hence, $$mAB=84$$,$$mBC=9$$−$$85$$−$$4=1$$,$$mCD=9$$−$$15$$−$$1=84$$,$$mAD=1$$,$$mAC=95$$,$$mBD=8$$−$$14$$−$$1=73Hence$$, the final figure will be a parallelogram.

$A rectangle A B C D, where A \equiv (0, 0), B \equiv (4, 0), C \equiv (4, 2), D \equiv (0, 2), undergoes the following transformations successively:$
$i. f_{1} (x, y) \to (y, x)$
$ii. f_{2} (x, y) \to (x + 3 y, y)$
$iii. f_{3} (x, y) \to ((x - y) / 2, (x + y) / 2)$
The final figure will be

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A rectangle ABCD, where 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−y)/2,(x+y)/2)The final figure will be

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$A rectangle A B C D, where A \equiv (0, 0), B \equiv (4, 0), C \equiv (4, 2), D \equiv (0, 2), undergoes the following transformations successively:$
$i. f_{1} (x, y) \to (y, x)$
$ii. f_{2} (x, y) \to (x + 3 y, y)$
$iii. f_{3} (x, y) \to ((x - y) / 2, (x + y) / 2)$
The final figure will be