The image you uploaded contains a geometric problem. Here's a breakdown of the questions:

1. Draw the figure and place the points C and D such that the vector $\overrightarrow{OC} = 3 \times \overrightarrow{OA}$ and $\overrightarrow{OD} = 3 \times \overrightarrow{OB}$.
2. Calculate the coordinates of points C and D.
3. Let I and J be the midpoints of segments [AB] and [CD], respectively. Determine the coordinates of I and J.
4. Show that the points O, I, and J are aligned.

I will first begin by helping you solve the first part of the problem, and then we can proceed step by step.

Step 1: Drawing the figure

We are given the following coordinates for points A and B:

• $A(1, 3)$
• $B(2, -5)$

Now, to place points C and D:

• Vector $\overrightarrow{OC}$ is three times $\overrightarrow{OA}$. So, the coordinates of C will be three times the coordinates of A.
• Vector $\overrightarrow{OD}$ is three times $\overrightarrow{OB}$. So, the coordinates of D will be three times the coordinates of B.

I'll start by calculating the coordinates of C and D.Let's calculate the coordinates of points C and D using the given information:

1. For point C: Since $\overrightarrow{OC} = 3 \times \overrightarrow{OA}$, the coordinates of point C are obtained by multiplying the coordinates of point A by 3: $\overrightarrow{OA} = (1, 3)$ Therefore: $\overrightarrow{OC} = 3 \times (1, 3) = (3, 9)$ So, the coordinates of point C are $C(3, 9)$.

2. For point D: Since $\overrightarrow{OD} = 3 \times \overrightarrow{OB}$, the coordinates of point D are obtained by multiplying the coordinates of point B by 3: $\overrightarrow{OB} = (2, -5)$ Therefore: $\overrightarrow{OD} = 3 \times (2, -5) = (6, -15)$ So, the coordinates of point D are $D(6, -15)$.

Now that we have the coordinates of C and D, the next step is to calculate the midpoints I and J, and then verify if the points O, I, and J are aligned.

Would you like me to proceed with that calculation?