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: First translation for point V

Apply $(x,y)\to(x + 3,y + 1)$ to $V(-6,-4)$.
$x=-6,y = - 4$; $x_1=-6 + 3=-3,y_1=-4 + 1=-3$. So $V$ becomes $V_1(-3,-3)$.

Step2: Second translation for new - V

Apply $(x,y)\to(x - 6,y - 4)$ to $V_1(-3,-3)$.
$x=-3,y=-3$; $x_2=-3-6=-9,y_2=-3 - 4=-7$. So the final image of $V$ is $V'(-9,-7)$.

Step3: First translation for point W

Apply $(x,y)\to(x + 3,y + 1)$ to $W(-3,1)$.
$x=-3,y = 1$; $x_3=-3 + 3=0,y_3=1 + 1=2$. So $W$ becomes $W_1(0,2)$.

Step4: Second translation for new - W

Apply $(x,y)\to(x - 6,y - 4)$ to $W_1(0,2)$.
$x = 0,y=2$; $x_4=0-6=-6,y_4=2 - 4=-2$. So the final image of $W$ is $W'(-6,-2)$.

Step5: Graph the segments

Graph the original segment $\overline{VW}$ with endpoints $V(-6,-4)$ and $W(-3,1)$ and the image segment $\overline{V'W'}$ with endpoints $V'(-9,-7)$ and $W'(-6,-2)$ on the given coordinate - grid.

Answer:

The original segment $\overline{VW}$ has endpoints $V(-6,-4)$ and $W(-3,1)$. The image segment $\overline{V'W'}$ after the composition of translations has endpoints $V'(-9,-7)$ and $W'(-6,-2)$. Graph both segments on the provided grid.