If `A(x, y), B (1, 2) and C (2, 1)` are the vertices of a triangle of area 6 square units, show that `x+y=15` or `-9`.

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) 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 the vertices of a triangle then excentre with respect to B is

If A (-3, 2) , B(x, y) and C(1, 4) are the vertices of an isosceles triangle with AB=BC . Find the value of (2x+y) .

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

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 the area of DeltaABC with vertices A(x,y),B(1,2)and C(2,1) is 6 square units, then prove that x + y = 15 or x + y + 9=0.

The points A (x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3)) are the vertices of Delta ABC . What are coordinate of the centroid of the triangle ABC ?

If the area of hat harr ABC formed by A(x,y),B(1,2) and C(2,1) is 7 squae units,then prove that x+y=15 or,x+y+9=0