4. Based on the centroid theorem, point Z is the centroid of triangle EGO.
5. If the length of GU is 18 units, the length of GZ is 12 units.
6. If the length of ZT is 4.8 units, the length of OT is 14.4 units.
In Mathematics and Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.
Part 4.
Based on the centroid theorem, we can logically deduce that point Z represents the centroid of triangle EGO.
Part 5.
If the length of GU is 18 units, the length of GZ can be calculated as follows;
GZ = 2/3 × GU
GZ = 2/3 × 18
GZ = 2 × 6
GZ = 12 units.
Part 6.
If the length of ZT is 4.8 units, the length of OT can be calculated as follows;
ZT = 1/3 × OT
4.8 = OT/3
OT = 4.8 × 3
OT = 14.4 units.