A triangle has its three sides equal to `a , b and c` . If the coordinates of its vertices are `A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3),` show that `|[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)`

A triangle has its three sides equal to a , b and c . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2) \ a n d \ C(x_3,y_3), show that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

A triangle has its three sides equal to a , ba n dc . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3), show that |(x_1,y_1,2),(x_2,y_2,2),(x_3,y_3, 2)|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

A triangle has its three sides equal to a,b and c. If the co-ordinates of its vertices are A(x_1y_1),B(x_2,y_2) and C(x_3,y_3) , show that {:|(x_1,y_1,2),(x_2,y_2,2),(x_3,y_3,2)|^2 = (a+b+c)(b+c-a)(c+a-b)(a+b-c)

A traingle has its three sides equal to a,b and c . If the co-ordinates of its vertices are A(x_(1),y_(1)) , B(x_(2),y_(2)) and C(x_(3),y_(3)) , show that : |{:(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2):}|^(2)=(a+b+c)(b+c-a)(c+a-b)(a+b-c) .

The centroid of the triangle with vertices at A(x_(1),y_(1)),B(x_(2),y_(2)),c(x_(3),y_(3)) is

The centroid of the triangle formed by A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) is

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC 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]|^2=3a^4

suppose that the mid point of the sides BC,CA and AB of a triangle Delta ABC are (5,7,11), (0,8,5) and (2,3,-1) If the vertices of the triangle are A(x_1,y_1,z_1), B(x_2,y_2,z_2) and C(x_3,y_3,z_3) derive nine equations in x_1,x_2,x_3,y_1,y_2,y_3,z_1,z_2, and z_3