Question

The line joining two points $A(2,0),B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of ${15}^{\circ }.$ Find the equation of the line in the new position. If $B$ goes to $C$ in the new position, what will be the coordinates of $C$ ?

Answer 1

A(2, 0) B (3, 1)

$m_{AB}=\frac{1-0}{3-2}=1\Rightarrow m=1\Rightarrow {45}^{\circ }$

angle of inclination of AC = ${60}^{\circ }$

r = AB = AC

$r=\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$

$r=\sqrt{2}$

coordinate of c $(rcos{60}^{\circ },rsin{60}^{\circ })$

$(\sqrt{2}\times \frac{1}{2},\sqrt{2}\times \frac{\sqrt{3}}{2})$

$(\frac{1}{\sqrt{2}},\frac{\sqrt{3}}{\sqrt{2}})$