The length of the perpendicular line - segment from origin to line $x - \sqrt{3} y + 4 = 0$ is _______.

-1

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Solution

The correct option is B 2
We use point to a line distance formula,

$d = \frac{| A m + B n + C |}{\sqrt{A^{2} + B^{2}}}$

Given,

point $(0, 0)$

line $x - \sqrt{3} y + 4 = 0$

$d = \frac{| (0) - \sqrt{3} (0) + 4 |}{\sqrt{1^{2} + (- \sqrt{3})^{2}}}$

$= \frac{4}{\sqrt{4}}$

$= 2$

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The length of the perpendicular line - segment from origin to line x−√3y+4=0 is _______.

The correct option is B 2We use point to a line distance formula,d=|Am+Bn+C|√A2+B2Given,point (0,0)line x−√3y+4=0d=|(0)−√3(0)+4|√12+(−√3)2=4√4=2

The length of the perpendicular line - segment from origin to line $x - \sqrt{3} y + 4 = 0$ is _______.

The correct option is B 2
We use point to a line distance formula,

$d = \frac{| A m + B n + C |}{\sqrt{A^{2} + B^{2}}}$

Given,

point $(0, 0)$

line $x - \sqrt{3} y + 4 = 0$

$d = \frac{| (0) - \sqrt{3} (0) + 4 |}{\sqrt{1^{2} + (- \sqrt{3})^{2}}}$

$= \frac{4}{\sqrt{4}}$

$= 2$