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#2 2012-12-14 03:11:27
- bob bundy
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Re: Triangle PQR
hi jacks
Hhhmmm. This is a new problem for me. But I suppose you could tackle it like this:
centroid: is at the intersection of the medians (which join the midpoint of a side to the opposite vertex, and is also one third of the way up any median.
So if P and Q have rational coordinates so will the midpoint of PQ.
R is also rational so the point one third of the way up from PQ towards R will be rational.
How does that sound to you?
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#4 2012-12-14 07:20:52
- bob bundy
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Re: Triangle PQR
Ok. Let's say P is (a,b) Q is (c,d) and R is (e,f)
a,b,c,d,e and f are all rational ie they are fractions
Midpoint PQ
and centroid is
the {rationals} are closed for +, - , x and ÷
ie. adding two fractions, or subtracting one fraction from another, or multiplying two fractions or dividing them will always give another fracftion.
Therefore both the midpoint and the centroid have rational coordinates.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei