Gegeben: $A(-1\mathrm{\mid }2)A(-1|2)$, $\overrightarrow{AB}=\left(\begin{array}{c}2\\ -3\end{array}\right)\backslash overrightarrow\{AB\}=\backslash begin\{pmatrix\}\; 2\; \backslash \backslash \; -3\; \backslash end\{pmatrix\}$

Gesucht: $B(b_1\mathrm{\mid }{b}_2)B(b\_1|b\_2)$

$\overrightarrow{AB}=\backslash overrightarrow\{AB\}=$$B-AB-A$

$B=A+\overrightarrow{AB}B=A+\backslash overrightarrow\{AB\}$

Setze die entsprechenden Werte ein:

$\left(\begin{array}{c}{b}_1\\ b_2\end{array}\right)=\left(\begin{array}{c}-1\\ 2\end{array}\right)+\left(\begin{array}{c}2\\ -3\end{array}\right)=\left(\begin{array}{c}1\\ -1\end{array}\right)\backslash begin\{pmatrix\}\; b\_1\; \backslash \backslash b\_2\; \backslash end\{pmatrix\}=\backslash begin\{pmatrix\}\; -1\; \backslash \backslash 2\; \backslash end\{pmatrix\}+\backslash begin\{pmatrix\}\; 2\; \backslash \backslash -3\; \backslash end\{pmatrix\}=\backslash begin\{pmatrix\}\; 1\; \backslash \backslash -1\; \backslash end\{pmatrix\}$

Die Koordinaten des Punktes $BB$ sind $B(1\mathrm{\mid }-1)B(1|-1)$.