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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?

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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
x4 is a x-coordinate and y4 is a y-coordinate on a triangle. –  ben Nov 6 '12 at 7:53

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