What is the centre of mass?

Four identical spheres each of mass $m$ are placed at the corners of a square of side $2 \, m$. Taking the point of intersection of the diagonals as the origin,the coordinates of the centre of mass are

$A$ rigid body consists of a $3 \ kg$ mass and a $2 \ kg$ mass connected by a massless rod. The $3 \ kg$ mass is at $\vec{r}_1 = (2 \hat{i} + 5 \hat{j}) \ m$ and the $2 \ kg$ mass is at $\vec{r}_2 = (4 \hat{i} + 2 \hat{j}) \ m$. Find the length of the rod and the coordinates of the center of mass.

Which of the following statements regarding the centre of mass is $NOT$ true?

Four particles of masses $m, 2m, 3m, 4m$ are placed at the corners of a square of side $a$ as shown in the figure. Find the coordinates of the center of mass.

Mass is distributed uniformly over a thin rectangular plate,and the positions of two vertices are given by $(1, 3)$ and $(2, -4)$. What is the position of the $3^{rd}$ vertex if the centre of mass of the plate lies at the origin?