Solving Rational Operations Questions

[ber8]

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

 

[tiny-tim]

welcome to pf!

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!

 

[ber8]

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

 

[tiny-tim]

easy!

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

 

[ber8]

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