Question

The line joining two points A (2, 0), B (3, 1) is rotated about A in anti - clockwise direction through an angle of ${15}^{\circ }$. Then the equation of the line in the new position if B goes to C in the new position, is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

The slope of the line AB is given by $m=\frac{1-0}{3-2}=1$

$\Rightarrow 1=tan\theta \Rightarrow \theta =\frac{\pi }{4}$
$\therefore$ The line makes on angle of ${45}^{\circ }$ with x-axis.
Now, AB is rotated through ${15}^{\circ }$.So, it makes an angle of ${60}^{\circ }$ with x – axis Therefore, the equation of AC is
$\frac{x-2}{cos{60}^{\circ }}=\frac{y-0}{sin{60}^{\circ }}$
$\Rightarrow \frac{x-2}{\frac{1}{2}}=\frac{y}{\frac{\sqrt{3}}{2}}$
Hence, (b) is the Correct Answer.