The dilation rule DF,3(x, y) is applied to △ABC, where the center of dilation is at F(1, 1). The distance in the x-coordinates from A(–2, 2) to the center of dilation F(1, 1) is unit(s). The distance in the y-coordinates from A(–2, 2) to the center of dilation F(1, 1) is unit(s). The vertex A' of the image is .

Answer:The distance between x-coordinates of A and F is 3 units.The distance between y-coordinates of A and F is 1 unit. The coordinates of A' are (-8,4).Step-by-step explanation:The dilation rule is [tex]D_{F,3}(x,y)[/tex].It means the center of dilation is F and scale factor is 3.The coordinates of A are (-2,2) and the coordinates of F are (1,1).The distance in the x-coordinates from A(–2, 2) to the center of dilation F(1, 1) is[tex]-2-1=-3[/tex]The distance can not be negative. So, the distance between x-coordinates of A and F is 3 units.The distance in the y-coordinates from A(–2, 2) to the center of dilation F(1, 1) is[tex]2-1=1[/tex]The distance between y-coordinates of A and F is 1 unit.According to given dilation rule,[tex](x,y)\rightarrow (3(x-1)+1,3(y-1)+1)[/tex]The coordinates of A' are[tex]A(-2,2)\rightarrow A'(3(-2-1)+1,3(2-1)+1)[/tex][tex]A(-2,2)\rightarrow A'(3(-3)+1,3(1)+1)[/tex][tex]A(-2,2)\rightarrow A'(-8,4)[/tex]Therefore the distance between x-coordinates of A and F is 3 units.The distance between y-coordinates of A and F is 1 unit. The coordinates of A' are (-8,4).