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The image contains a geometric diagram and questions related to projections of points in a 3D coordinate system. I will go through the questions one by one and interpret the diagram to provide the correct answers.

### Given Questions and Diagram:

1. **На якій відстані від осі OY перебуває точка D (Рис.1)?**
   - This question asks for the distance of point **D** from the **OY** axis.
   - From the diagram, point **D** is located along the **Z**-axis at position **D₃**, and its projection onto the **XOY** plane is **D₂**.
   - To find the distance from **OY**, we need to look at the projection of **D** onto the **XOZ** plane, which is along the **X** axis. Hence, the distance from the **OY** axis is the **X-coordinate** of **D** (marked as **D₂** in the diagram).

2. **Де розміщена точка, яка має X=0, Y=0, Z≠0?**
   - This question refers to a point where **X = 0** and **Y = 0**, but **Z ≠ 0**.
   - In the diagram, such a point would lie on the **Z-axis**. Hence, it is point **A₃**, which lies on the **Z-axis** above the origin.

3. **Записати координати точки M (Рис.1).**
   - We need to find the coordinates of point **M** in the diagram.
   - Point **M** is projected onto the planes **XOY**, **YOZ**, and **XOZ** as **M₁**, **M₂**, and **M₃** respectively. Based on these projections, the coordinates of point **M** can be determined.
   - Coordinates of **M** would be: \((x_M, y_M, z_M)\).

4. **Які з точок лежать на осях проекцій (Рис.1)?**
   - The points that lie on the projection axes are the points that have one or more coordinates equal to zero.
   - Based on the diagram, points like **A₁**, **K₁**, **K₂**, **K₃** appear to be on the projection axes.

5. **Як називається площина проекцій П₃ (Рис.1)?**
   - This asks for the name of the projection plane **П₃** in the diagram.
   - From the diagram, **П₃** is the **YOZ** plane, as it is perpendicular to the **X-axis**.

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### Answers Based on Interpretation:

1. **Distance of point D from the OY-axis**: The distance is along the **X-axis**, indicated by the **D₂** projection of **D**.

2. **Location of the point with X = 0, Y = 0, Z ≠ 0**: Point **A₃** lies on the **Z-axis**.

3. **Coordinates of point M**: Based on the diagram, the coordinates of point **M** are \((M₁, M₂, M₃)\), where these represent its projections.

4. **Points lying on projection axes**: Points such as **A₁**, **K₁**, **K₂**, **K₃** lie on the axes of projections.

5. **Name of projection plane П₃**: The projection plane **П₃** is the **YOZ plane**.

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Let me know if you would like further details or have any specific questions.

### Follow-up questions:
1. What are the steps to calculate the distance of a point from an axis in a 3D coordinate system?
2. How can you determine the coordinates of a point using its projections on the coordinate planes?
3. What are the properties of points lying on coordinate axes?
4. Can you explain how the different projection planes are defined in 3D space?
5. How are 3D coordinates used in practical applications of engineering or architecture?

### Tip:
In 3D geometry, projections onto planes (such as **XOY**, **YOZ**, and **XOZ**) help simplify complex spatial relationships into more manageable 2D views, which are often used in technical drawing and CAD modeling.

Analyze the geometric diagram with related questions concerning projections of points in a 3D coordinate system.

Explore detailed explanations and solutions for projecting points in a 3D coordinate system, featuring analysis of point distances, plane identification, and coordinate determinations. This resource is suitable for university-level students and educators interested in advanced geometry.

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