Write the formula for the area of the triangle having its vertices at `(x_1,\ y_1),\ \ (x_2,\ y_2)` and `(x_3,\ y_3)` .

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

Find the coordinates of the centroid of a triangle having vertices P(x_1,y_1,z_1),Q(x_2,y_2,z_2) and R(x_3,y_3,z_3)

The area of the triangle OAB with vertices O(0,0),A(x_(1),y_(1))B(x_(2),y_(2)) is

The area of the triangle OAB with vertices O(0,0),A(x_(1),y_(1))" and B(x_(2),y_(2)) is

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

The co-ordinates of incentre of the triangle whose vertices are given by A(x_(1), y_(1)), B(x_(2), y_(2)), C(x_(3), y_(3)) is

If the co-ordinates of the vertices of an equilateral triangle with sides of length a are (x_1,y_1), (x_2, y_2), (x_3, y_3), then |[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]|=(3a^4)/4

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)