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.

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:

  1. What is the significance of each axis in this 3D coordinate system?
  2. How are the positive and negative axes defined in 3D space?
  3. Can you explain the role of the origin (O) in determining coordinates?
  4. What happens to the coordinates when a point lies on more than one axis?
  5. 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