Four vertices of a tetrahedron are (0,0,0),(4,0,0),(0,−8,0) and (0,0,12). Its centroid has the coordinates
A tetrahedron is a three dimensional figure bounded by non coplanar triangular planes. So a tetrahedron has four non-coplanar points as its vertices. Suppose a tetrehedron has points A,B,C,D as it vertices which have coordinates (x1,y1,z1),(x2,y2,z2) , (x3,y3,z3) and (x4,y4,z4) respectively in a rectangular three dimensional space. Then the coordinates of its centroid are [x1+x2+x3+x44,y1+y2+y3+y44,z1+z2+z3+z44]. Let A tetrahedron has three of its vertices represented by the points (0,0,0),(6,5,1) and (4,1,3) and its centroid lies at the point (1,2,5). Now answer the following two questions. The equation of the traingular plane of tetrahedron that contains the given vertices
Find the coordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (8, 0). [2 MARKS]
If a triangle has its orthocenter at (1, 1) and circumcenter at (32,34) , then the coordinates of the centroid of the triangle are