The problem asks to place points $A$, $B$, and $C$ on a line $\Delta$ equipped with a Cartesian coordinate system $(O, \overrightarrow{OI})$. The specific locations of $A$, $B$, and $C$ are not provided in the cropped image. Therefore, I cannot answer the problem. More information regarding how to locate these points is needed.

1. Problem Description

The problem asks to place points $A$, $B$, and $C$ on a line $\Delta$ equipped with a Cartesian coordinate system $(O, \overrightarrow{OI})$. The specific locations of $A$, $B$, and $C$ are not provided in the cropped image. Therefore, I cannot answer the problem. More information regarding how to locate these points is needed.

2. Solution Steps

Since the coordinates of $A$, $B$, and $C$ are missing, I cannot proceed with the solution. If for instance we are given that $OA=1$, $OB=2$, and $OC=3$ relative to the origin $O$, we can place $A$ at the point $1$, $B$ at the point $2$, and $C$ at the point $3$ on the line.

3. Final Answer

Cannot answer the question because information is missing regarding the positions of the points $A, B, C$ on the line $\Delta$.