Question 200404
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The distance from a point to a line is the length of the line segment between the given point and the point of intersection of a line perpendicular to the given line that contains the given point with the given line.


Step 1:  Solve the given equation for *[tex \Large y] to put the equation into slope intercept form (this is already done for you), then determine the slope of the given line by inspection of the coefficient on *[tex \Large x].


Step 2:  Use


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2} \text{ and } m_1, m_2 \neq 0]


to calculate the slope of a line perpendicular to the given line.


Step 3:  Write an equation of the line perpendicular to the given line that passes through the given point using the point-slope form of the equation of a line:


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


Step 4:  Using the equation of the given line and the equation of the line just derived in step 3, solve the system of equations for the point of intersection.


Step 5:  Use the distance formula to calculate the distance between the point of intersection derived in Step 4 and the given point.


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


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