Question

Use the given coordinates, scale factor, and center of dilation to fill in the blanks.3, AC-1,-1), D (0.2), 7(3,1), scale factor 2,

Answer 1

We have that the general rule for a dilation is:

$D_k(x,y)=(kx,ky)_{}$

where k is the scale factor.

In this case, we have the following:

$\begin{gathered} k=2 \\ \Rightarrow D_2(x,y)=(2x,2y) \end{gathered}$

then, if we apply this transformation on points A, D and I, we have:

$\begin{gathered} D_2(A)=D_2(-1,-1)=(2(-1),2(-1))=(-2,-2)=A^{\prime} \\ D_2(D)=D_2(0,2)=(2(0),2(2))=(0,4)=D^{\prime} \\ D_2(I)=D_2(3,1)=(2(3),2(1))=(6,2)=I^{\prime} \end{gathered}$

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