two proofs

klreed2

New member
Joined
Jun 24, 2005
Messages
9
One,

Show that the diagonals of a parallelogram bisect eachother.


Two,

Given 4 arbitrary points, z1,z2,z3,z4 in the complex plane, let w1,

w2, w3, w4 be centroids of triangle(tri) z2z3z4 ; tri z1z3z4 ; tri

z1z2z4 ; tri z1z2z3 respectively. Show that the four line segments

joining the points z1 and w1, z2 and w2, and z3 and w3, z4 and w4

intersect at one point.


Thanks
 
klreed2 said:
One,
Show that the diagonals of a parallelogram bisect eachother.
Two,
Given 4 arbitrary points, z1,z2,z3,z4 in the complex plane, let w1,
w2, w3, w4 be centroids of triangle(tri) z2z3z4 ; tri z1z3z4 ; tri
z1z2z4 ; tri z1z2z3 respectively. Show that the four line segments
joining the points z1 and w1, z2 and w2, and z3 and w3, z4 and w4
intersect at one point. Thanks

One: have you actually tried?

Two: if you don't know enough to "try #1", then this one
is way out of your league...
 
Denis, that is a great answer!
When someone asks two such disparate questions, I wonder what is going on.
I would not take the time to do the tedious steps to show the second.
It may not even be true: the points must be such that no three are collinear.
I have to wonder why it is set in the complex plane.
It must be noted that this is a double post on this site.
It has also been posted on at least two other help sites.
 
ONE - I have tried them both. The first problem needs to be proven with complex numbers, but I forgot to say that.

TWO - Who cares if the problems are different? What does that matter?

THREE - YES I posted this twice on this site - I really wanted help with it, and yes I posted on another website. Who cares? This way I have better chance of getting help. Maybe I missed the point of the help forum.

FOUR - I don't think "this problem is way out of my league so I can't solve it" would suffice as an answer for my teacher. But maybe I'll try and see what happens.



[/b]
 
FIVE - This question has not been posted on at least two other websites. Only ONE other - but thanks for checking.
 
FAIR ENOUGH!
But what about my point, “the points must be such that no three are collinear.”
Is that part of the statement? If not the proposition is FALSE!

Why are these couched in terms of complex variables?
Do you have some special way of finding a centroid for a triangular region in the complex plane? I have taught complex analysis for a long time but I remain ignorant of any such method which is special to complex numbers.

P.S. Are you using Steve Krantz's text?
 
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