Question

The coordinate axes is rotated and shifted in such a way that the $I{V}^{th}$ quadrant direction of line $4x+3y-35=0$ becomes the new positive $x$ -axis direction and the $I^{st}$ quadrant direction of line $3x-4y+5=0$ becomes the new positive $y$ -axis direction. If origin as per old coordinate system is $O,$ then according to the new coordinate system, the coordinates of $O$ are

• A. $\left(1,7\right)$
• B. $\left(-1,7\right)$
• C. $\left(1,-7\right)$
• D. $\left(7,-1\right)$

Answer 1

Answer: (C)

Distance of $\left(0,0\right)$ from lines $4x+3y-35=0$ (new $x$ -axis) and $3x-4y+5=0$ (new $y$ -axis) are $7$ units and $1$ unit respectively.
Since, according to the new coordinate system $O$ lies in $I{V}^{th}$ quadrant, hence the new coordinates of $O$ are $\left(1,-7\right)$ .