Question

The perpendicular distance from the origin to a line is 7 and the perpendicular makes an angle of ${150}^{\circ }$ with the positive x-axis. Find the equation of the line.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Equation of the line in the normal form is:

$xcos\alpha +ysin\alpha =p$

Here, give $p=7$

$\alpha ={150}^{\circ }$

$cos\alpha =cos{150}^{\circ }=cos({180}^{\circ }-{30}^{\circ })=-cos{30}^{\circ }=\frac{-\sqrt{3}}{2}$

$sin\alpha =sin{150}^{\circ }=sin({180}^{\circ }-{30}^{\circ })=sin{30}^{\circ }=\frac{1}{2}$

Equation of the line is:

$x\left(\frac{-\sqrt{3}}{2}\right)+y\left(\frac{1}{2}\right)=7$

$-\sqrt{3}x+y=14$

$-\sqrt{3}x+y-14=0$