Parallelverschiebung

Abbildungsgleichung der Parallelverschiebung

Somit ergibt sich $\overrightarrow{O{P}^{\mathrm{\prime }}}=\overrightarrow{OP}+\vec{v}=\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}{v}_x\\ v_y\end{array}\right)\backslash overrightarrow\{OP\text{'}\}=\backslash overrightarrow\{OP\}+\backslash vec\{\; v\}=\backslash begin\{pmatrix\}x\backslash \backslash y\backslash end\{pmatrix\}+\backslash begin\{pmatrix\}v\_x\backslash \backslash v\_y\backslash end\{pmatrix\}$.

Koordinatenform:

$x^{\mathrm{\prime }}=x+v_{x}x\text{'}=\; x+v\_x$

$y^{\mathrm{\prime }}=y+v_{y}y\text{'}=y+v\_y$

Matrixform:

Beispiel

Verschiebe den Punkt $P(3\mathrm{\mid }2)P(3|2)$ um den Vektor $\vec{v}=\left(\begin{array}{c}-5\\ 3\end{array}\right)\backslash vec\{v\}=\backslash begin\{pmatrix\}-5\; \backslash \backslash 3\backslash end\{pmatrix\}$.