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.

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.

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.