Question

Suppose $P$ is a point with coordinates $(-8,3)$ with respect to a coordinate system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$. Let $X_1^{{}^{\prime }}{O}_1{X}_1\leftrightarrow Y_1^{{}^{\prime }}{O}_1{Y}_1$ be another system with $X^{\prime }OX\parallel X_1^{{}^{\prime }}{O}_1{X}_1$ and suppose $O_1$ has coordinates $(9,5)$ with respect to $X^{\prime }OX\leftrightarrow Y^{\prime }OY$. What are the coordinates of $P$ in the system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$?

Answer 1

In $X^{\prime }OX\leftrightarrow Y^{\prime }OY$ system, $O_1=(9,5)$

Since, $X_1^{\prime }{O}_1{X}_1$ and $Y_1^{\prime }{O}_1{Y}_1$ intersect at $O_1$. So, in $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ system $O_1$ is the origin and thus, takes the value $(0,0)$.

In $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ system, the origin $O$ has the value $(-9,-5)$ and thus, co-ordinates of $P$ will be $(-9+(-8),-5+3)$ which is same as $(-17,-2)$.

Hence, co-ordinates of $P$ are $(-17,-2)$.