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Given a parallelogram with vertices A(- 2, - 1), B(4, 2), C(7, 7) and D(1, 4).
a. Find the equation of a parallelogram as a function of x.
b. Prove that the given parallelogram is real a parallelogram.
Solution:
The first that we have to do is to plot the vertices of a parallelogram and draw the figure as well.
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a. To get the equation of a parallelogram as a function of x, we need to get the equations of the sides of the parallelogram using the two point form.
For AB, substitute the values of points A and B
For BC, substitute the values of points B and C
For CD, substitute the values of points C and D
For DA, substitute the values of points D and A
Therefore, the equation of a parallelogram as a function of x is
b. Since the slopes of the opposite sides of a parallelogram are equal, then the given parallelogram is real a parallelogram.
mAB = mCD = ½
mBC = mDA = 5/3