# Finding x-coordinate of a triangle

If we assume that s1(x)=s2(x) (the areas of the two triangles are equal) and and we know (x1, y1), (x2, y2), (x3, y3)and also we assume that the line L which is between (x1, y1) and (x4, y4), because we know for example another point in this line so we know the slope and the line. How can I find x4 ?

At fisrt , I want to find (x(x4), y(x4)) (intersection of two triangles) , so we have: (y2-y1/x2-x1)(x-x1) + y1 = (y3-y4/x3-x4)(x-x3)+ y3 then we should solve this equation to find x and y in terms of x4. Then by equality of areas of two triangles, could we find x4? could some body help me to find x4?

Your use of symbols is quite confusing to me. E.g., is x4 a coordinate, or a triangle, and if it is a triangle, then what is y4? –  MvG Nov 6 '12 at 6:28