Question

Point A is on the line y+3x=2 and is equidistant from points B and C, both of which lie on the line y=1/3x+8. D is on the intersection of both lines. Prove that y+3x=2 bisects BC.

Answer 1

AC=BC, that means, that
Sqrt((Ay-Cy)^2+(Ax-Cx)^2=Sqrt((By-Cy)^2+(Bx-Cx)^2), hence
Sqrt((2-3Ax-1/3Cx-8)^2+(Ax-Cx)^2=Sqrt((2-3Bx-1/3Cx-8)^2+(Bx-Cx)^2)
Hence, we see, that the only point, that is satisfying thisequation are points, that are equidistant from line intersection.
That means, line is bisecting BC