Login 
RegisterForget your password?
Equation of Simpson's Line
May 5, 2009 - 11:01am
A(6, 4), B(2, -4), and C(-5, 0) are vertices of triangle ABC. Point D on the circumcircle of ABC is midway between arc AB, and point E is on the line AB. If line DE is perpendicular to line AB, find the equation of the Simpson's line through E.
May 27, 2009 - 3:05pm
#2
Re: Equation of Simpson's Line
Here is what I've got from Googling: http://mathforum.org/library/drmath/view/55115.html
My solution to this problem:
- Find the coordinates of E, it is the midpoint of AB.
- Determine the equations of the following: Circle through A, B, and C with center O; Line AB; Line BC; Line AC; and Line DE.
- Find the coordinates of D by the equations of DE and the circumcircle.
- Drop a line from D perpendicular to AC, the intersection is point F, determine the equation of DF then find the coordinates of F.
- Use the two points E and F to determine the equation of the Simpson's Line.
To check your work
- Extend the line CB to H to establish the line BH.
- Drop a perpendicular to BH from point D, the intersection point is G.
- Find the coordinates of G
- Substitute the coordinates of G to the Simpson's line, the equation must be satisfied by that coordinates of G.
Anybody are welcome to post their answer. Good luck.
Wow, ang tindi. First time ko na encounter ang Simpson's line. I try to Google it.