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(B) The perpendicular distance $d$ from a point $(x_1, y_1)$ to the line $Ax + By + C = 0$ is given by the formula: $d = \frac{|Ax_1 + By_1 + C|}{\sqr

Vedclass · Accepted Answer

$1$

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(B) The perpendicular distance $d$ from a point $(x_1, y_1)$ to the line $Ax + By + C = 0$ is given by the formula: $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Here,the point is the origin $(0, 0)$,so $x_1 = 0$ and $y_1 = 0$.The equation of the line is $\sqrt{3}x - y + 2 = 0$,where $A = \sqrt{3}$,$B = -1$,and $C = 2$.Substituting these values into the formula:$d = \frac{|\sqrt{3}(0) - (0) + 2|}{\sqrt{(\sqrt{3})^2 + (-1)^2}}$$d = \frac{|2|}{\sqrt{3 + 1}}$$d = \frac{2}{\sqrt{4}}$$d = \frac{2}{2} = 1$.Thus,the length of the perpendicular is $1$.

Find the length of the perpendicular drawn from the origin to the line $\sqrt{3}x - y + 2 = 0$.

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