Rational Operations

  • Thread starter ber8
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  • #1
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Hi guys, I'm having trouble solving the following questions.

1) Show that the line through two rational points has an equation with rational coefficients

2) show that a circle whose center is a rational point and whose radius is rational has an equation with rational coefficient.

Cheers
 

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi ber8! welcome to pf! :wink:

you need to find the equations …

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
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this is what i did for (1)

If two points have rational coefficients (a,b) and (c,d), the line between them has equation:

x(b-d) - y(a-c) = (bc - ad)

this is where I'm stuck. I'm not sure how to proof the coefficients of the equation are rational
 
  • #4
tiny-tim
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easy! :smile:

just write a = p/q (where p and q are integers) etc :wink:
 
  • #5
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Wow. I didn't think of that! Thanks very much :D
 

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