A(2,b) translation T_1 = (((−3)),(( b)) ) followed by translation T_2 = ((a),(4) ) A′=(b−1,a−3) determine the value of a+b=...?


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Question Number 8528 by suci last updated on 14/Oct/16

$A (2, b) t r a n s l a t i o n T_{1} = (\begin{matrix} - 3 \\ b \end{matrix})$ $f o l l o w e d b y t r a n s l a t i o n T_{2} = (\begin{matrix} a \\ 4 \end{matrix})$ $A^{'} = (b - 1, a - 3)$ $d e t e r m i n e t h e v a l u e o f a + b = . . . ?$
	Answered by sandy_suhendra last updated on 14/Oct/16

	$2 - 3 + a = b - 1 \Rightarrow a - b = 0 . . . . (1)$ $b + b + 4 = a - 3 \Rightarrow a - 2 b = 7 . . . . (2)$ $(1) - (2) \Rightarrow b = - 7 and a = - 7$ $so a + b = - 7 - 7 = - 14$
	Answered by 666225 last updated on 15/Oct/16

	$a n s w e r$ $- 3 + a = 2 \equiv a = 5 . . (A)$ $s u b .$ $- 3 + a = b - 1 . . (A^{'})$ $- 3 + 5 = b - 1 \equiv b = 3$ $b + 4 = b \equiv 2 b = 4 \equiv b = 2 . . (A)$ $s u b .$ $b + 4 = a - 3 . . (A^{'})$ $2 + 4 = a - 3 \equiv a = 7$ $\Rightarrow a + b = (5 + 7) + (3 + 2) = 17$
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