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)`

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)

Theorem : The area of a triangle the coordinates of whose vertices are (x_1;y_1);(x_2;y_2)and (x_3;y_3) is 1/2|(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|

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

Prove that the coordinates of the centre of the circle inscribed in the triangle,whose vertices are the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) are (ax_(1)+bx_(2)+cx_(3))/(a+b+c) and (ay_(1)+by_(2)+cy_(3))/(a+b+c)

Find the value of (x, y), if centroid of the triangle with coordinates (x, 0), (0, y) and (6,3) is (3,4).

The coordinates of the orthocentre of the triangle formedby the lines 2x^(2)-3xy+y^(2)=0 and x+y=1 are

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4