Exercise 6 Page 177

We want to use the given translations to find the image $\overline{V^{\prime \prime }{W}^{\prime \prime }}.$ We should begin by plotting the endpoints of the preimage, $V(\text{-}6,\text{-}4)$ and $W(\text{-}3,1),$ on a coordinate plane.

Next, we can do the first of the given translations, $(x,y)\to (x+3,y+1).$ This translation tells us that we should add $3$ to the $x\text{-}$coordinates and $1$ to the $y\text{-}$coordinates. Let's add these new points to the same coordinate plane. Now, we can translate the new image, $\overline{V^{\prime }{W}^{\prime }},$ using the second of the given translations, $(x,y)\to (x-6,y-4).$ We need to subtract $6$ from the $x\text{-}$coordinates and $4$ from the $y\text{-}$coordinates. Finally, we can use these new coordinates to draw the image $\overline{V^{\prime \prime }{W}^{\prime \prime }}.$

We can remove the intermediate image so that we can see only the preimage and the image after the composition of the translations.