Question

Suppose $P$ has coordinates $(10,2)$ in a coordinate system $X^{\prime }OX-Y^{\prime }OY$ and $(-3,-6)$ in another coordinate system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ with $X^{\prime }OX\parallel X_1^{\prime }{O}_1{X}_1$. Determine the coordinates of $O$ with respect to the system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$

Answer 1

$P$ has coordinates $(10,2)$ in a coordinate system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$ and $(-3,-6)$ in coordinate system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$

$O_1$ has coordinate $(0,0)$ in coordinate system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$.

In $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ coordinate system, $x$-coordinate of $O$ will be $-3-10=-13$ and $y$-coordinate will be $-6-2=-8$.

Thus, the coordinates of $O$ in $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ coordinate system will be $(-13,-8)$.