Question

If the line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in anticlock wise direction through an angle of ${15}^{\circ }$. Find the equation of the line in new position.

Answer 1

The slope of the line $AB$ is

$\frac{1-0}{3-2}=1$ or $\tan {45}^{\circ }$

After rotation of the line through ${15}^{\circ }$, the slope of the line $AC$ in new position is tan{{60}^{\circ}}=\sqrt{3}$

$\therefore$ the equation of the new line $AC$ is

$y-0=\sqrt{2}(x-2)$

or $y-\sqrt{3}x+2\sqrt{3}=0$