Question 244194
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Presuming that the sides of the parallelogram are the segments AB, BC, CD, and DA, proceed thusly:


Compute the slope of the line containing the segment AB using the slope formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} ]


Where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the endpoints of the segment.


Write an equation of the line that passes through point D with a slope equal to the slope of the line that contains the segment AB using the point-slope form of the equation of a line:


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


Where *[tex \Large m] is the slope you just calculated and *[tex \Large \left(x_2,y_2\right)] are the coordinates of D.  Call this equation 1.


Repeat the above steps with respect to line segment BC and point D.  Call this equation 2.


Solve the system of equations formed by equations 1 and 2.  The solution set will be the desired coordinates of the fourth vertex.


Do your other problem the same way.



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