First slide

Equation of line in Straight lines

Question

If a line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through
an angle 15º, then equation of the line in the new position is

Moderate

A

$\sqrt{3} x + y = 2 \sqrt{3}$
B

$\sqrt{3} x - y = 2 \sqrt{3}$
C

$x + \sqrt{3} y = 2 \sqrt{3}$
D

$x - \sqrt{3} y = 2 \sqrt{3}$

Solution

Slope of AB $= \frac{1 - 0}{3 - 2} = 1$
$\Rightarrow ∠ B A X = 45^{\circ} (Ref. Fig. 16.18)$
If AC is the new position of the line AB then $∠ C A X = 45^{\circ} + 15 º = 60 º$
and thus its equation is
$\begin{array}{l} y = \tan 60^{\circ} (x - 2) \\ y = \sqrt{3} (x - 2) \Rightarrow \sqrt{3} x - y = 2 \sqrt{3} \end{array}$

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