$2.$ Consider the diagram, Find the homogeneous transformations $\backslash (\backslash$mathrm$\{$H$\}01,\backslash$mathrm$\{$H$\}02,\backslash$mathrm$\{$H$\}12\backslash )$ representing the transformations among the three frames shown. Show that $\backslash (\backslash$mathrm$\{$H$\}02=\backslash$mathrm$\{$H$\}01*\backslash$mathrm$\{$H$\}12\backslash ).(10$ Points$)$

Extra Credit $(5$ Points$)$

$1.$ Try to develop a homogeneous transform $\backslash ($ H$\_\{2\}^\{1\}\backslash )$ from frame $1$ to frame $2,$ by translating along the hypotenuse of the right triangle shown in the figure.

Hint: Step $\backslash (1-\backslash )$ Align an axis of your choice such that it is collinear with the hypotenuse Step $2-$ Translate along the hypotenuse

Step $3-$ Undo Step $1($advisable but not necessary$)$

Step $\backslash (4-\backslash )$ Align frames $1$ and $2.$