The line joining two points A(2,0), B(3,1) is rotated about A in … - Vidyadip

MCQ

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

✓
$\sqrt 3 x - y - 2\sqrt 3 = 0$
B
$x - 3\sqrt y - 2 = 0$
C
$\sqrt 3 x + y - 2\sqrt 3 = 0$
D
$x + 3\sqrt y - 2 = 0$

✓

Answer

Correct option: A.

$\sqrt 3 x - y - 2\sqrt 3 = 0$

a
(a) Here slope of $AB = \frac{1}{1} \Rightarrow \tan \theta = {m_1} = 1$or $\theta = {45^o}$.
Thus slope of new line is $\tan ({45^o} + {15^o}) = \tan {60^o} = \sqrt 3 $
{It is rotated anticlockwise so the angle will be ${45^o} + {15^o} = {60^o}$}
Hence the equation is $y = \sqrt 3 x + c$, but it still passes through (2,0), hence $c = - 2\sqrt 3 $.
Thus required equation is

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