Question 1125228: Quadrilateral ABCD has coordinates A(2,3) B(7,10) C(9,4) and D(4,-3). Prove that quadrilateral ABCD is a parallelogram but not a rhombus
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Using the slope formula,  where ) and ) are the coordinates of two points:
Calculate the slopes of the six lines that contain the following segments:  ,  ,  ,  ,  , and  .
If ABCD is a parallelogram, then  will be parallel to  so the line segments containing those segments will have equal slopes. Further,  will be parallel to  and those segments will lie in lines that have equal slopes.
If ABCD was a rhombus, then the lines containing segments  and  would be perpendicular. But if they are not perpendicular, but do intersect, then the parallelogram is NOT a rhombus. Hence the slopes of the diagonals must not be equal to each other and also not be negative reciprocals of each other.
So, in summary, you need to show (where  is the slope of  )
John
My calculator said it, I believe it, that settles it
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