Question

If a point $P$ has coordinates $(3,4)$ in a coordinate system $X^{\prime }OX\leftrightarrow Y^{\prime }OY$, and if $O$ has coordinates $(4,3)$ in another system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ with $X^{\prime }OX\parallel X_1^{\prime }{O}_1{X}_1$, then the coordinates of $P$ in the new system $X_1^{\prime }{O}_1{X}_1\leftrightarrow Y_1^{\prime }{O}_1{Y}_1$ is ________________

• A. $(3,4)$
• B. $(1,-1)$
• C. $(7,7)$
• D. $(-1,1)$

Answer 1

Answer: (C)

$(7,7)$

Given the point P has coordinate (3,4).Similarly O has (4,3)

Given that $X^{\prime }OX\leftrightarrow Y^{\prime }OY{X}_1^{{}^{\prime }}{O}_1{X}_1\leftrightarrow Y_1^{{}^{\prime }}{O}_1{Y}_1⟹X^{{}^{\prime }}OX\parallel X_1^{{}^{\prime }}{O}_1{X}_1$

$\therefore$ Coordinate of P in new system $X_1^{{}^{\prime }}O{X}_1\leftrightarrow Y_1^{{}^{\prime }}O{Y}_1=(3+4,)=(7,7)$