Question

find a translation that has the same effect as the composition of translations below. t_(4,1)(x,y) followed by t_(-5,7)(x,y)
choose the correct answer below.
a. (x,y)→(x + 9,y - 6)
b. (x,y)→(x - 1,y - 6)
c. (x,y)→(x + 9,y + 8)
d. (x,y)→(x - 1,y + 8)

Explanation:

Step1: Apply first translation

The translation $T_{(4,1)}(x,y)$ moves a point $(x,y)$ to $(x + 4,y+1)$.

Step2: Apply second translation

Applying $T_{(- 5,7)}$ to the result of the first - translation. If the point after the first translation is $(x + 4,y + 1)$, then after the second translation, it becomes $(x+4-5,y + 1+7)$.

Step3: Simplify the coordinates

Simplify $(x+4-5,y + 1+7)$ to get $(x-1,y + 8)$.

Answer:

D. $(x,y)\to(x - 1,y + 8)$