If $$Ax1$$,$$y1$$,$$Bx2$$,$$y2$$,$$Cx3$$,$$y3$$ are the vertices of a triangle, then the $$equationxy1x1y11x2y21$$ $$+xy1x1y11x3y31$$ $$=0represents$$

Correct option is 3the median through A

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$If A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3}) are the vertices of a triangle, then the equation |\begin{matrix} x & y & 1 \\ x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \end{matrix}| + |\begin{matrix} x & y & 1 \\ x_{1} & y_{1} & 1 \\ x_{3} & y_{3} & 1 \end{matrix}| =0$ represents

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the altitude throught A

the perpendicular bisector of side BC

the median through A

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Correct option is C

The given equation becomesxy1x1y11x2+x3y2+y32=0⇒xy1x1y11x2+x32y2+y321=0It is the equation of the line passing through A and mid point of BC.

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If Ax1,y1,Bx2,y2,Cx3,y3 are the vertices of a triangle, then the equationxy1x1y11x2y21 +xy1x1y11x3y31 =0represents

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$If A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3}) are the vertices of a triangle, then the equation |\begin{matrix} x & y & 1 \\ x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \end{matrix}| + |\begin{matrix} x & y & 1 \\ x_{1} & y_{1} & 1 \\ x_{3} & y_{3} & 1 \end{matrix}| =0$ represents