Vector translation

\begin{pmatrix}x\\y\end{pmatrix} + \begin{pmatrix}a\\b\end{pmatrix} = \begin{pmatrix}x+a\\y+b\end{pmatrix}

They can be represented by vectors, but not by matrices, because the origin moves.

Translate the point (1,0) by vector \begin{pmatrix}4\\-1\end{pmatrix}

• x_1=1
• y_1=0
• \Delta x=4
• \Delta y=-1
• x_2=x_1+\Delta x=1+4=5
• y_2=y_1+\Delta y=0+(-1)=-1
• New point is (5,-1)

Translate the point (-2,3) by vector \begin{pmatrix}-1\\2\end{pmatrix}

• x_1=-2
• y_1=3
• \Delta x=-1
• \Delta y=2
• x_2=x_1+\Delta x=-2+(-1)=-3
• y_2=y_1+\Delta y=3+2=5
• New point is (-3,5)

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