Question

graph $overline{vw}$ with endpoints $v(-6, - 4)$ and $w(-3,1)$ and its image after the composition. translation: $(x,y)\to(x + 3,y + 1)$ translation: $(x,y)\to(x - 6,y - 4)$

Explanation:

Step1: Apply first translation to point V

For point $V(-6,-4)$, using $(x,y)\to(x + 3,y + 1)$, we get $V_1=(-6+3,-4 + 1)=(-3,-3)$.

Step2: Apply second translation to $V_1$

Using $(x,y)\to(x - 6,y - 4)$ on $V_1(-3,-3)$, we get $V_2=(-3-6,-3-4)=(-9,-7)$.

Step3: Apply first translation to point W

For point $W(-3,1)$, using $(x,y)\to(x + 3,y + 1)$, we get $W_1=(-3+3,1 + 1)=(0,2)$.

Step4: Apply second translation to $W_1$

Using $(x,y)\to(x - 6,y - 4)$ on $W_1(0,2)$, we get $W_2=(0-6,2-4)=(-6,-2)$.

Answer:

The endpoints of the image of $\overline{VW}$ are $V_2(-9,-7)$ and $W_2(-6,-2)$.