Matplotlib - Plot a plane and points in 3D simultaneously

Just elaborating a little more on the math part (and how it works), may be useful for someone, the equation of a plane with unit normal vector n containing a point a is shown as follows:

so that the equation of the plane here is x + y + 2*z = 9 and the following code can simply be used to plot the given plane:

# create the figure
fig = plt.figure()

# add axes
ax = fig.add_subplot(111,projection='3d')

xx, yy = np.meshgrid(range(10), range(10))
z = (9 - xx - yy) / 2 

# plot the plane
ax.plot_surface(xx, yy, z, alpha=0.5)

plt.show()

Plotting the point is straightforward with scatter()

Just to add to @suever's answer, you there's no reason why you can't create the Axes and then plot both the surface and the scatter points on it. Then there's no need to use ax.hold():

# Create the figure
fig = plt.figure()

# Add an axes
ax = fig.add_subplot(111,projection='3d')

# plot the surface
ax.plot_surface(xx, yy, z, alpha=0.2)

# and plot the point 
ax.scatter(point2[0] , point2[1] , point2[2],  color='green')

You will need to tell the axes that you want new plots to add to the current plots on the axes rather than overwriting them. To do this, you will need to use axes.hold(True)

# plot the surface
plt3d = plt.figure().gca(projection='3d')
plt3d.plot_surface(xx, yy, z, alpha=0.2)

# Ensure that the next plot doesn't overwrite the first plot
ax = plt.gca()
ax.hold(True)

ax.scatter(points2[0], point2[1], point2[2], color='green')

UPDATE

As @tcaswell pointed out in the comments, they are considering discontinuing support for hold. As a result, a better approach may be to use the axes directly to add more plots as in @tom's answer.