Question

A point $P$ has coordinates $(7,10)$ in a coordinate system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$. Suppose it has coordinates $(10,7)$ in another coordinate system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ with $X^{\prime }OX\leftrightarrow X_1^{\prime }{O}_1{X}_1$. Find the coordinates of $O_1$ in the system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$.

Answer 1

$P$ has coordinates $(7,10)$ in a coordinate system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$.

Also, it has coordinates $(10,7)$ in a coordinate system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$.

So, $X_1^{\prime }{O}_1{X}_1$ intersect $X^{\prime }OX$ at the point $7-10=-3$ and $Y_1^{\prime }{O}_1{Y}_1$ intersect $Y^{\prime }OY$ at the point $10-7=3$

Thus, $X_1^{\prime }{O}_1{X}_1$ and $Y_1^{\prime }{O}_1{Y}_1$ intersect each other at the point $(-3,3)$ in coordinate system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$ and $O_1$ has coordinates $(-3,3)$.

Hence, coordinates of $O_1$ in th system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$ is $(-3,3)$.