If Ax1,y1,Bx2,y2,Cx3,y3 are the vertices ofa triangle, then the equation   x    y    1x1    y1    1x2    y2    1+x    y    1x1    y1    1x3    y3    1=0 represents

The given equation can be written asxy1−y2+y1−y3−yx1−x2+x1−x3                     +x1y2−x2y1+x1y3−y1x3=0⇒x2y1−y2−y3−y2x1−x2−x3+y12x1−x2−x3−x12y1−y2−y3=0⇒y−y1=2∣y1−y2−y32x1−x2−x3x−x1which represents the median through A.