Math Problem Statement
За даними на малюнку 283 визначте координати точок: 1) А, В, С, D, Е, F; 2) K, L, M, N, О, Р.
Solution
Based on the 3D coordinate system shown in the image, I will determine the coordinates of the points requested:
1) Coordinates of points A, B, C, D, E, F:
- A: Located at (-2, 0, 0) on the negative X-axis.
- B: Located at (0, 0, -2) on the negative Z-axis.
- C: Located at (1, 0, 0) on the positive Y-axis.
- D: Located at (1, 2, 0) in the YZ-plane.
- E: Located at (0, 2, 0) on the positive Z-axis.
- F: Located at (-1, 0, 0) on the negative X-axis.
2) Coordinates of points K, L, M, N, O, P:
- K: Located at (-2, 0, 0) on the negative X-axis.
- L: Located at (0, 0, -1) between O and B on the Z-axis.
- M: Located at (2, 0, 0) on the positive Y-axis.
- N: Located at (2, 1, 0) in the YZ-plane.
- O: Origin at (0, 0, 0).
- P: Located at (-1, 0, 0) on the negative X-axis (the same as point F).
Would you like a detailed explanation of how these coordinates were identified, or do you have any other questions?
Follow-up Questions:
- What is the significance of each axis in this 3D coordinate system?
- How are the positive and negative axes defined in 3D space?
- Can you explain the role of the origin (O) in determining coordinates?
- What happens to the coordinates when a point lies on more than one axis?
- How would you describe a point that lies on a plane, like the XY-plane, in terms of coordinates?
Tip:
When interpreting coordinates in 3D, remember that each point is represented by three numbers (x, y, z), which correspond to the position along the X, Y, and Z axes respectively.
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Math Problem Analysis
Mathematical Concepts
3D Coordinate System
Geometry
Formulas
Coordinate formula (x, y, z)
Theorems
Basic properties of the 3D coordinate plane
Suitable Grade Level
Grades 9-11
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