I am trying to solve the following question:
I have created the scaling, translation and rotation matrices that I feel will transform the left figure to the figure on the right:
Scaling $$ \begin{pmatrix} 1 & 0 & 0 \\ 0 & 0.5 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} $$ Translation $$ \begin{pmatrix} 1 & 0 & -5 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} $$ Rotation $$ \begin{pmatrix} -\sqrt{3}/2 & 0.5 & 0 \\ -0.5 & -\sqrt{3}/2 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} $$
However, when I do the matrix multiplication for the matrices I have created, I don't get any of the options listed. The correct answer is supposed to be B. Where have I gone wrong?
Your answer should be given by scaling * rotation * translation. But your rotation matrix is wrong. From the figure, you need to rotate the object by -$\pi/3$, so your rotation matrix is $$\begin{pmatrix}0.5 && \sqrt 3 /2&&0\\-\sqrt 3 /2&& 1/2 &&0\\0&&0&&1\end{pmatrix}$$