- #1

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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

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- Thread starter ber8
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- #1

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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

- #2

tiny-tim

Science Advisor

Homework Helper

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hi ber8! welcome to pf!

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!

- #3

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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

Science Advisor

Homework Helper

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easy!

just write a = p/q (where p and q are integers) etc

just write a = p/q (where p and q are integers) etc

- #5

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Wow. I didn't think of that! Thanks very much :D

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