Question

find a translation that has the same effect as the composition of translations below. t_(2, - 3)(x,y) followed by t_(-4,8)(x,y) choose the correct answer below. a. (x,y)→(x + 6,y - 5) b. (x,y)→(x - 2,y - 5) c. (x,y)→(x + 6,y + 11) d. (x,y)→(x - 2,y + 11)

Explanation:

Step1: Analyze the first translation

The translation $T_{(2,3)}(x,y)$ means adding 2 to the $x$ - coordinate and 3 to the $y$ - coordinate. So, $(x,y)\to(x + 2,y+3)$.

Step2: Analyze the second translation

The translation $T_{(-4,8)}(x,y)$ means adding - 4 to the $x$ - coordinate and 8 to the $y$ - coordinate. After the first - translation, we have $(x + 2,y + 3)$. Applying the second translation:
The new $x$ - coordinate is $(x + 2)+(-4)=x+2 - 4=x - 2$.
The new $y$ - coordinate is $(y + 3)+8=y+3 + 8=y + 11$.
So the composition of the two translations is $(x,y)\to(x - 2,y + 11)$.

Answer:

D. $(x,y)\to(x - 2,y + 11)$