We should first recognize that a dilation by a scale factor of 1/2 is actually a compression.
We are told the compression is done about the point (2,1):
What we should do is translate the whole figure so the origin is the point about which we do the compression. To do this, we subtract 2 from the x-coordinate of each vertex and we subtract 1 from the y-coordinate of each vertex.
With this in mind, to coordinates of the translation (TA, TB, TC) will be:
[tex]TA^{^{}}=(-6-2,-3-1)=(-8,-4)[/tex][tex]TB=(4-2,-1-1)=(2,-2)[/tex]
[tex]TC=(2-2,7-1)=(0,6)[/tex]
Now we multiply this new coordinates by the scale factor to obtain a new set of coordinates (A'', B'', C''):
[tex]A^{\doubleprime}=\frac{1}{2}(-8,-4)=(-4,-2)[/tex][tex]B^{\doubleprime}=\frac{1}{2}(2,-2)=(1,-1)[/tex][tex]C^{\doubleprime}=\frac{1}{2}(1,6)=(0,3)[/tex]
Finally, we translate the figure back were we started, so we add 2 to the x-coordinate and 1 to the y-coordinate to obtain A', B' and C':
[tex]A^{\prime}=(-4+2,-2+1)=(-2,-1)[/tex][tex]B^{\prime}=(1+2,-1+1)=(3,0)[/tex][tex]C^{\prime}=(0+2,3+1)=(2,4)[/tex]
