The first thing we have to do is calculate the 1/3 dilation for our initial figure. For this each of our points must be multiplied by the scale factor
[tex]\begin{gathered} A(0,6)\to(0,2) \\ B(-3,-6)\to(-1,-2) \\ C(-9,-6)\to(-3,-2) \\ D(-12,-3)\to(-4,-1) \end{gathered}[/tex]
Graphically you can see the initial points in blue are dilated forming the figure in green
Now to carry out the translation along the vector <-5, -1>, what we must do is transform our Point A into the end point of the vector, that is, into the point (-5, -1) and perform the same calculations for the other points
[tex]\begin{gathered} A^{\prime}(0,-2)\to(-5,-1) \\ B^{\prime}(-1,-2)\to(-6,-5) \\ C^{\prime}(-3,-2)\to(-8,-5)^{} \\ D^{\prime}(-4,-1)\to(-9,-4)^{} \end{gathered}[/tex]
Finally, the translated and dilated graph can be seen in red
