When we dilate a figure centered at the origin by a factor k, the new coordinates will be equal to the old coordinates multiplied by the scale factor.
[tex](x,y)\to(kx,ky)[/tex]
The original vertices of our figure are:
[tex]L(0,0),M(-4,1),N(-3,-6)[/tex]
Then, dilating our figure with a scale factor equal to -3, we have:
[tex]\begin{gathered} L(0,0)\to L^{\prime}((-3)\cdot0,(-3)\cdot0)=L^{\prime}(0,0) \\ M(-4,1)\to M^{\prime}((-3)\cdot(-4),(-3)\cdot1)=M^{\prime}(12,-3) \\ N(-3,-6)\to N^{\prime}((-3)\cdot(-3),(-3)\cdot(-6))=N^{\prime}(9,18) \end{gathered}[/tex]
The coordinates of the image are
[tex]L^{\prime}(0,0),M^{\prime}(12,-3),N^{\prime}(9,18)[/tex]
