Hi
You have these points:
The slope of the line is:
Now consider a general point of this line, which must have the same slope:
Now you got it
Greetings
Hi,
I'm stuck on a problem and I need help... I'm supposed to find the general equation of a line (Ax+By+C=0) from two points. I did a couple of these problems and everything went well but not for this one... so here goes:
points: (-sqrt(2)/2, sqrt(2)/2), (1/2, sqrt(3)/2)
We are given the answer but I can't figure out how to get there... Here is the answer:
(sqrt(3) - sqrt(2))x - (1 + sqrt(2))y + (sqrt(2) + sqrt(6)) / 2 = 0
Anyone can help me with the steps to get to this answer?
This is my first post so go easy on me if there is a better way to format equations (just tell me how to).
Thanks!
Hi and thanks for your answer.
I'm pretty new to maths so what might seem obvious for you is still a mystery for me
I did understand the slope formula but I can't see why the y difference (sqrt(3) - sqrt(2)) transfers to the A variable in Ax+By+C=0 (same thing for the x difference that becomes B...) Also, how you get the C variable from these differences is beyond me.
Sorry if this is too much explanation to have me understand something simple but I just don't get it
Thanks
You give the equation as Ax+ By= C. Do you realize those numbers are not "unique"? You could multiply the entire equation by any constant. You could, for example, Divide the entire equation by C to get (A/C)x+ (B/C)y= 1. Rewriting that as A'x+ B'y= 1 (A'= A/C and B'= B/C), putting , we have and multiplying both sides by , .
Now put x= 1/2, in the equation: so that . Now, subtracting the previous equation from that, the A' is eliminated: . Solve that for B', then put that into either of the previous equations.