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`.

The coordinates of the vertices of a triangle are (4, -3), (-5, 2) and (x, y). If the centroid of the triangle is at the origin, show that x=y=1 .

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 Delta ABC 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.

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

Show that the points A (5, 6), B(1,5), C(2, 1) and D(6, 2) are the vertices of a square ABCD.

Show that the points A (5,6) B (1,5) and C (2,1) and D (6,2) are the vertices of a square ABCD.

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.

If the area of A B C formed by A(x , y),B(1,2)a n dC(2,1) is 6 squae units, then prove that x+y=15or ,x+y+9=0

Two vertices of triangle are (2,-1) and (3,2) and third vertex lies on the line x+y=5. If the area of the triangle is 4 square units, then the third vertex is a. (0,50) or (4,1) b. (5,0) of (1,4) c. (5,0) or (4,1) d. (o,5) or (1,4)