Respuesta :
By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.
If there is a reduction, then 0 < k < 1.
If there is an enlargement, then k > 1.
[tex](x,y)\rightarrow(kx,ky)[/tex]So, you have
[tex]\begin{gathered} (5,-1)\rightarrow(5\cdot2,-1\cdot-2)=(10,2) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}[/tex][tex]\begin{gathered} (1,1)\rightarrow(6\cdot1,6\cdot1)=(6,6) \\ \text{In this case, k = 6 and k > 1 then the coordinate points have an enlargement} \\ (6,6)\rightarrow(\frac{1}{6}\cdot6,\frac{1}{6}\cdot6)=(1,1) \\ \text{In this case, k = 1 and 0< k < 1 then the coordinate points have an reduction} \end{gathered}[/tex][tex]\begin{gathered} (4,9)\rightarrow(4\cdot5,9\cdot\frac{34}{9})=(20,34) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}[/tex][tex]\begin{gathered} (3,0)\rightarrow(3\cdot3,3\cdot0)=(9,0) \\ \text{In this case, k = 3 and k > 1 then the coordinate points have an enlargement} \\ (9,0)\rightarrow(2\cdot9,2\cdot0)=(18,0) \\ \text{In this case, k = 2 and k > 1 then the coordinate points have an enlargement} \end{gathered}[/tex][tex]\begin{gathered} (0,-5)\rightarrow(-1\cdot0,-1\cdot-5)=(0,5) \\ \text{ In this case, k = -1, and by definition k > 0} \end{gathered}[/tex]Therefore, the correct answer is
[tex]B\text{.}(1,1)\rightarrow(6,6)\rightarrow(1,1)[/tex]