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 the translation $(x,y)\to(x + 3,y + 1)$:
$x=-6,y = - 4$
$x_1=-6 + 3=-3,y_1=-4 + 1=-3$
So $V$ becomes $V_1(-3,-3)$

Step2: Apply second translation to $V_1$

Using the translation $(x,y)\to(x - 6,y - 4)$ on $V_1(-3,-3)$
$x=-3,y=-3$
$x_2=-3-6=-9,y_2=-3 - 4=-7$
The final image of $V$ is $V'(-9,-7)$

Step3: Apply first translation to point W

For point $W(-3,1)$, using the translation $(x,y)\to(x + 3,y + 1)$:
$x=-3,y = 1$
$x_3=-3 + 3=0,y_3=1 + 1=2$
So $W$ becomes $W_1(0,2)$

Step4: Apply second translation to $W_1$

Using the translation $(x,y)\to(x - 6,y - 4)$ on $W_1(0,2)$
$x=0,y=2$
$x_4=0-6=-6,y_4=2 - 4=-2$
The final image of $W$ is $W'(-6,-2)$

Answer:

The endpoints of the original segment are $V(-6,-4)$ and $W(-3,1)$. The endpoints of the image segment after the composition of translations are $V'(-9,-7)$ and $W'(-6,-2)$. To graph, first plot $V$ and $W$ and draw the segment $\overline{VW}$. Then plot $V'$ and $W'$ and draw the segment $\overline{V'W'}$.