If `A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)` are the vertices of the triangle then show that:`

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

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 |x y1x_1y_1 1x_2y_3 1|+|x y1x_1y_1 1x_3y_3 1|=0 represents (a)the median through A (b)the altitude through A (c)the perpendicular bisector of B C (d)the line joining the centroid with a vertex

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 |x y1x_1y_1 1x_2y_3 1|+|x y1x_1y_1 1x_3y_3 1|=0 represents (a)the median through A (b)the altitude through A (c)the perpendicular bisector of B C (d)the line joining the centroid with a vertex

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of triangleABC ,find the coordinates of the centroid of the triangle.

If A(x_(1),y_(1)),B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices of a triangle then excentre with respect to B is

If (x_1,y_1) , (x_2,y_2) and (x_3,y_3) are the vertices of a triangle whose area is k square units, then |{:(x_1,y_1,4),(x_2,y_2,4),(x_3,y_3,4):}|^2 is

If A(3x_(1),3y_(1)),B(3x_(2),3y_(2)),C(3x_(3),3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+x_(2)+x_(3),y_(1)+y_(2)+y_(3)) then the /_ABC=

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4