Question 199380
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The given line is already in slope-intercept form, so you can determine the slope by inspection.  Determine the slope of a line perpendicular to the given line by calculating the negative reciprocal of the slope of the given line.


Use the point-slope form of the equation of a line to determine the equation of a line perpendicular to the given line that passes through the origin.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y - y_1 = m(x - x_1) ]


Where *[tex \Large m] is the negative reciprocal of the slope of the given line and *[tex \Large \left(x_1,y_1\right)] is the origin, (0,0).


The given line and its perpendicular through the origin form a system of equations.  Solve the system for the point of intersection.


Finally use the distance formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d = sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}]


Where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the point of intersection and the origin to calculate the distance from the origin to the given line.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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