Question 373979: A(-5, 0), B(-3,4), C(3,0), D(-2,-4)
i need to see if those points make a parallelorgram, what is the faster way without graphing?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! A(-5, 0), B(-3,4), C(3,0), D(-2,-4)
If they made a parallelogram, you'd have to show that both pairs of opposite
sides are parallel.
So why not graph them? Then you'd see that ABCD is not a parallelogram immediately:
If we connect all the points we have 6 line segments
To do it without graphing you'd have find the slopes of all 6 pairs of points
to see if there are two pairs with the same slopes. That's because without
graphing you can't tell which pairs of points are the endpoints of the
sides and which are the endpoints of the diagonals. So you'd have to find all
six to see if two pairs have the same slope. Here's what you'd have to do
without graphing:
slope of AB
slope of AC
slope of AD
slope of BC
slope of BD
slope of CD
Then you'd look among the 6 slopes and find that there are not two pairs of
lines with the same slopes, which there would have to be if ABCD were a
parallelogram. You are always better off graphing. For then if you can't tell
just by looking that it's not a parallelogram, you'd at least know which two
are diagonals and you won't have to bother finding the slopes of the two
diagonals.
Edwin
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