Answer
${G_2}\left( {u,v} \right) = \left( {2 + 4u + 2v,2 + u + 3v} \right)$
${G_3}\left( {u,v} \right) = \left( { - 1 + 4u + 2v,1 + u + 3v} \right)$
Work Step by Step
1. The translate ${G_2}$
Using Figure 15, we see that $a=2$, $b=2$. Therefore,
${G_2}\left( {u,v} \right) = \left( {2 + 4u + 2v,2 + u + 3v} \right)$
2. The translate ${G_3}$
Using Figure 15, we see that $a=-1$, $b=1$. Therefore,
${G_3}\left( {u,v} \right) = \left( { - 1 + 4u + 2v,1 + u + 3v} \right)$