Solution:
Given the coordinates of triangle ABC below;
[tex]A(-9,-6),\text{ }B(-3,3)\text{ and }C(0,-3)[/tex]
For point matrix ABC, the formula is
[tex]=\begin{bmatrix}{-9} & {-3} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {-6} & {3} & {-3}\end{bmatrix}[/tex]
After dilation by a factor of 2/3, the matrix becomes
[tex]\begin{gathered} =\begin{bmatrix}{\frac{2}{3}}\cdot-9 & {\frac{2}{3}}\cdot-3 & {\frac{2}{3}}\cdot0 \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {\frac{2}{3}}\cdot-6 & {\frac{2}{3}}\cdot3 & {\frac{2}{3}}\cdot-3\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {-4} & {2} & {-2}\end{bmatrix} \end{gathered}[/tex]
Hence, the answer is
[tex]\begin{bmatrix}{-6} & {-2} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} \\ {-4} & {2} & {-2}\end{bmatrix}[/tex]
