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

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

Area of the triangle formed by (x_(1),y_(1)),(x_(2),y_(2)),(3x_(2)-2x_(1),3y_(2)-2y_(1)) (in sq.units) is

Show that the coordinates off the centroid of the triangle with vertices A(x_(1),y_(1),z_(1)),B(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) are ((x_(1)+x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3),(z_(1)+z_(2)+z_(3))/(3))

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

Theorem: Prove that the coordinates of centroid of the triangle whose coordinates are (x_(1);y_(1));(x_(2);y_(2)) and (x_(3);y_(3)) are ((x_(1)+x_(2)+x_(3))/(3);(y_(1)+y_(2)+y_(3))/(3))

If |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=|{:(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1):}| , then the two triangles with vertices (x_(1),y_(1)) , (x_(2),y_(2)) , (x_(3),y_(3)) and (a_(1),b_(1)) , (a_(2),b_(2)) , (a_(3),b_(3)) must be congruent.

|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|=|(a_1,b_1,1),(a_2,b_2,1),(a_3,b_3,1)| then the two triangles with vertices (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) and (a_(1), b_(1)), (a_(2), b_(2)), (a_(3), b_(3)) are

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) .