We have that the general rule for a dilation is:
[tex]D_k(x,y)=(kx,ky)_{}[/tex]
where k is the scale factor.
In this case, we have the following:
[tex]\begin{gathered} k=2 \\ \Rightarrow D_2(x,y)=(2x,2y) \end{gathered}[/tex]
then, if we apply this transformation on points A, D and I, we have:
[tex]\begin{gathered} D_2(A)=D_2(-1,-1)=(2(-1),2(-1))=(-2,-2)=A^{\prime} \\ D_2(D)=D_2(0,2)=(2(0),2(2))=(0,4)=D^{\prime} \\ D_2(I)=D_2(3,1)=(2(3),2(1))=(6,2)=I^{\prime} \end{gathered}[/tex]
therefore, the points after the transformations are
A'=(-2,-2)
D'=(0,4)
I'=(6,2)
We have the following graph for the dilated figure:
where the green figure is the dilated figure with scale factor of 2
