Answer:
Option 3: (1,-2)
Step-by-step explanation:
From the given figure it is clear that the vertices of triangle ABC are A(1,4), B(1,1), C(4,1).
If a figure dilated by the factor k and the center of dilation is point (a,b), then the rule of dilation is
[tex](x,y)\rightarrow (k(x-a)+a,k(y-b)+b)[/tex]
The figure ABC dilated by the factor 2 and the center of dilation is point A(1,4).
[tex](x,y)\rightarrow (2(x-1)+1,2(y-4)+4)[/tex]
[tex](x,y)\rightarrow (2x-2+1,2y-8+4)[/tex]
[tex](x,y)\rightarrow (2x-1,2y-4)[/tex]
The coordinates of B after dilation are
[tex]B(1,1)\rightarrow B'(2(1)-1,2(1)-4)[/tex]
[tex]B(1,1)\rightarrow B'(1,-2)[/tex]
The coordinates of B after dilation are (1,-2).
Therefore, the correct option is 3.
