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Let (xr,yr) r = 1 ,2,3 are the coordina...

Let `(x_r,y_r) r = 1 ,2,3` are the coordinates of the vertices of a triangle ABC. If D is the point onit in the ratio of `1 : 2`. reckoning from the vertex B, prove that the equation of the line AD is `2|(x,y,1),(x_1,y_1,1),(x_2,y_2,1)|+|(x,y,1), (x_1, y_1, 1), (x_3,y_3,1)|=0`. Also find the equation of the line AE in the similar form where E is the harmonic conjugate of D wrt the points B and C.

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