In general, a dilation is the outcome of applying the following transformation on a point,
[tex]D(x,y)\to(kx,ky)[/tex]
Where k is the scale factor, this kind of dilation is about the origin, and we will use it since the problem does not specify otherwise.
In our case, the transformation is
[tex]D(x,y)\to(\frac{x}{2},\frac{y}{2})[/tex]
Then,
[tex]\begin{gathered} D(A)=D(-6,5)\to(-3,\frac{5}{2}) \\ D(B)=D(3,2)\to(\frac{3}{2},1)_{} \\ D(C)=D(0,-1)\to(0,-\frac{1}{2}) \end{gathered}[/tex]
On the other hand, a reflection over the x-axis is given by the following transformation.
[tex](x,y)\to R_x(x,y)=(x,-y)[/tex]
Then, in our case,
[tex]\begin{gathered} A^{\prime}=R_x(-3,\frac{5}{2})=(-3,-\frac{5}{2}) \\ B´=R_x(\frac{3}{2},1)=(\frac{3}{2},-1) \\ C^{\prime}=R_x(0,-\frac{1}{2})=(0,\frac{1}{2}) \end{gathered}[/tex]
Thus, the answers are
A'=(-3,-5/2)
B'=(3/2,-1)
C'=(0,1/2)
