Answer:
The correct option is 1.
Step-by-step explanation:
From the given figure it is clear that the vertices of triangle RST are
R(-6,10), T(-10,0) and S(-2,6).
The given composition is [tex]D_{0,\frac{3}{2}}(x,y)\circ D_{0,\frac{1}{2}}(x,y)[/tex], it means the figure dilated by factor 1/2 with center of dilation is origin, then the figure dilated by factor 3/2 with center of dilation is origin.
If a point dilated by factor k with center of dilation is origin, then
[tex](x,y)\rightarrow (kx,ky)[/tex]
The coordinates of S after dilation by factor 1/2 with center of dilation is origin is
[tex]S(-2,6)\rightarrow S'(\frac{1}{2}(-2),\frac{1}{2}(6))=S'(-1,3)[/tex]
The coordinates of S' after dilation by factor 3/2 with center of dilation is origin is
[tex]S'(-1,3)\rightarrow S''(\frac{3}{2}(-1),\frac{3}{2}(3))= S''(-\frac{3}{2},\frac{9}{2})[/tex]
The coordinates of S'' are [tex]S''(-\frac{3}{2},\frac{9}{2})[/tex]
Therefore the correct option is 1.
