https://file.aiquickdraw.com/mathbot/file/1727275707252k2moxhjv.jpg

The image asks for a sketch of the points \((0, 5, 2)\), \((4, 0, -1)\), \((2, 4, 6)\), and \((1, -1, 2)\) on a coordinate axis. These are points in 3D space with the format \((x, y, z)\).

Let me explain how to plot these points:

1. **Step 1: Identify the coordinate axes.**
   In 3D space, we use three axes:
   - \(x\)-axis (horizontal)
   - \(y\)-axis (vertical)
   - \(z\)-axis (typically perpendicular to the \(xy\)-plane)

2. **Step 2: Plot each point.**
   - **Point (0, 5, 2)**:
     - \(x = 0\) (on the origin for the \(x\)-axis),
     - \(y = 5\) (upward on the \(y\)-axis),
     - \(z = 2\) (outward from the \(xy\)-plane).
   
   - **Point (4, 0, -1)**:
     - \(x = 4\) (to the right on the \(x\)-axis),
     - \(y = 0\) (on the \(xy\)-plane),
     - \(z = -1\) (downward, below the \(xy\)-plane).

   - **Point (2, 4, 6)**:
     - \(x = 2\) (right on the \(x\)-axis),
     - \(y = 4\) (upward on the \(y\)-axis),
     - \(z = 6\) (far above the \(xy\)-plane).

   - **Point (1, -1, 2)**:
     - \(x = 1\) (slightly to the right),
     - \(y = -1\) (below the \(xy\)-plane),
     - \(z = 2\) (outward from the plane).

I can sketch this graph if you'd like me to generate the 3D coordinate plot. Would you like me to create a visual of this 3D plot?

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Here are 5 follow-up questions based on this task:
1. What are the coordinates of the origin in a 3D coordinate system?
2. How would you describe the relationship between the \(x\)-axis, \(y\)-axis, and \(z\)-axis in 3D space?
3. What kind of shape do these points form if connected?
4. How would these points change if translated by \((1, 1, 1)\)?
5. What is the distance between the points \((2, 4, 6)\) and \((1, -1, 2)\)?

**Tip**: Always remember to check the signs of each coordinate carefully when plotting points in 3D space!

Sketch the points (0, 5, 2), (4, 0, -1), (2, 4, 6), and (1, -1, 2) on a single set of coordinate axes.

Learn how to plot the points (0,5,2), (4,0,-1), (2,4,6), and (1,-1,2) on a 3D coordinate system. This task involves identifying coordinates on the x, y, and z axes, making it suitable for students in Grades 9-12 studying coordinate geometry.

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