Answer:
The correct option is 3. The image of X is X'(6,2).
Step-by-step explanation:
[tex]D_{Z,2}[/tex] means the dialation by scale factor 2 and the center of dilation is Z.
If a figure dilated by scale factor k and the center of dilation is (a,b), then
[tex](x,y)\rightarrow (k(x-a)+a,k(y-b)+b)[/tex]
From the given figure it is clear that the coordinates of X are (4,0) and the coordinates of Z are (2,-2), so the coordinates of image are
[tex]X(4,0)\rightarrow X'(2(4-2)+2,2(0+2)-2)[/tex]
[tex]X(4,0)\rightarrow X'(6,2)[/tex]
The image of X is X'(6,2). Therefore the correct option is 3.
