Straight Lines
Rotation of Line — New Equation
nta_pyq_2024_jan
Grade 11
Question:
A line passing through the point $A(9,0)$ makes an angle of $30°$ with the positive direction of $x$-axis. If this line is rotated about $A$ through an angle of $15°$ in the clockwise direction, then its equation in the new position is
$\dfrac{y}{\sqrt{3}-2}+x=9$
$\dfrac{x}{\sqrt{3}-2}+y=9$
$\dfrac{x}{\sqrt{3}+2}+y=9$
$\dfrac{y}{\sqrt{3}+2}+x=9$
Step-by-Step Solution
Key Concept: After clockwise rotation by $15°$, new angle $=30°-15°=15°$. New slope $=\tan15°=2-\sqrt3$. Equation: $y=(2-\sqrt3)(x-9)$.
$y=(2-\sqrt3)(x-9)\Rightarrow\frac{y}{\sqrt3-2}+x=9$.
Correct Answer: 1