The task is to plot the points $(1, 5, 3)$, $(0, 2, -3)$, $(-3, 0, 2)$, and $(2, -2, -1)$ in 3D space. Let me explain how to approach this:

Solution:

1. Coordinate Axes: Use a 3D Cartesian coordinate system where:

   • The $x$-axis represents the first coordinate,
   • The $y$-axis represents the second coordinate, and
   • The $z$-axis represents the third coordinate.

2. Points to Plot:

   • $(1, 5, 3)$: Move to $x=1$, $y=5$, and $z=3$.
   • $(0, 2, -3)$: Move to $x=0$, $y=2$, and $z=-3$.
   • $(-3, 0, 2)$: Move to $x=-3$, $y=0$, and $z=2$.
   • $(2, -2, -1)$: Move to $x=2$, $y=-2$, and $z=-1$.

3. Graph Representation: I'll generate a 3D plot for these points. One moment while I prepare the visualization. matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D

Points to plot

points = { "A (1, 5, 3)": (1, 5, 3), "B (0, 2, -3)": (0, 2, -3), "C (-3, 0, 2)": (-3, 0, 2), "D (2, -2, -1)": (2, -2, -1) }

Extract coordinates

x_coords = [p[0] for p in points.values()] y_coords = [p[1] for p in points.values()] z_coords = [p[2] for p in points.values()]

Plot

fig = plt.figure(figsize=(10, 8)) ax = fig.add_subplot(111, projection='3d')

Plot points

ax.scatter(x_coords, y_coords, z_coords, color='red', s=50, label='Points')

Annotate each point

for label, (x, y, z) in points.items(): ax.text(x, y, z, label, fontsize=9, color='blue')

Set labels and grid

ax.set_xlabel('X-axis') ax.set_ylabel('Y-axis') ax.set_zlabel('Z-axis') ax.set_title('3D Coordinate Plot of Given Points') ax.grid(True) plt.legend() plt.show()Here is the 3D plot of the points $(1, 5, 3)$, $(0, 2, -3)$, $(-3, 0, 2)$, and $(2, -2, -1)$ on a coordinate axis. Each point is labeled for clarity.

Would you like further clarification on the steps, or need help with any related questions?

5 Related Questions:

1. How can you calculate the distance between two points in 3D space?
2. What is the formula for finding the midpoint between two points in 3D space?
3. How do we determine if four points lie on the same plane?
4. Can you determine the equation of a plane that passes through three of these points?
5. How does plotting in 3D differ from 2D?

Tip:

When plotting in 3D, it helps to identify the orientation of the axes clearly to avoid confusion with coordinates!