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

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

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)| is equal to

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,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 represents

if (x_ (1), y_ (1)), (x_ (2), y_ (2)), (x_ (3), y_ (3)) are vertices equilateral triangle such that (x_ (1) -2) ^ (2) + (y_ (1) -3) ^ (2) = (x_ (2) -2) ^ (2) + (y_ (2) -3) ^ (2) = (x_ (3) - 2) ^ (2) + (y_ (3) -3) ^ (2) then x_ (1) + x_ (2) + x_ (3) +2 (y_ (1) + y_ (2) + y_ (3) ))

If A(x_1, y_1), B (x_2, y_2) and C (x_3, y_3) are the vertices of a DeltaABC and (x, y) be a point on the internal bisector of angle A , then prove that : b|(x,y,1),(x_1, y_1, 1), (x_2, y_2, 1)|+c|(x, y,1), (x_1, y_1, 1), (x_3, y_3, 1)|=0 where AC = b and AB=c .

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)=