Here is another way to draw a Cartesian coordinate system, built on the answers that have already been given.
import numpy as np # v 1.19.2
import matplotlib.pyplot as plt # v 3.3.2
# Enter x and y coordinates of points and colors
xs = [0, 2, -3, -1.5]
ys = [0, 3, 1, -2.5]
colors = ['m', 'g', 'r', 'b']
# Select length of axes and the space between tick labels
xmin, xmax, ymin, ymax = -5, 5, -5, 5
ticks_frequency = 1
# Plot points
fig, ax = plt.subplots(figsize=(10, 10))
ax.scatter(xs, ys, c=colors)
# Draw lines connecting points to axes
for x, y, c in zip(xs, ys, colors):
ax.plot([x, x], [0, y], c=c, ls="--", lw=1.5, alpha=0.5)
ax.plot([0, x], [y, y], c=c, ls="--", lw=1.5, alpha=0.5)
# Set identical scales for both axes
ax.set(xlim=(xmin-1, xmax+1), ylim=(ymin-1, ymax+1), aspect="equal")
# Set bottom and left spines as x and y axes of coordinate system
ax.spines['bottom'].set_position('zero')
ax.spines['left'].set_position('zero')
# Remove top and right spines
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
# Create 'x' and 'y' labels placed at the end of the axes
ax.set_xlabel('x', size=14, labelpad=-24, x=1.03)
ax.set_ylabel('y', size=14, labelpad=-21, y=1.02, rotation=0)
# Create custom major ticks to determine position of tick labels
x_ticks = np.arange(xmin, xmax+1, ticks_frequency)
y_ticks = np.arange(ymin, ymax+1, ticks_frequency)
ax.set_xticks(x_ticks[x_ticks != 0])
ax.set_yticks(y_ticks[y_ticks != 0])
# Create minor ticks placed at each integer to enable drawing of minor grid
# lines: note that this has no effect in this example with ticks_frequency=1
ax.set_xticks(np.arange(xmin, xmax+1), minor=True)
ax.set_yticks(np.arange(ymin, ymax+1), minor=True)
# Draw major and minor grid lines
ax.grid(which="both", color="grey", linewidth=1, linestyle="-", alpha=0.2)
# Draw arrows
arrow_fmt = dict(markersize=4, color="black", clip_on=False)
ax.plot((1), (0), marker=">", transform=ax.get_yaxis_transform(), **arrow_fmt)
ax.plot((0), (1), marker="^", transform=ax.get_xaxis_transform(), **arrow_fmt)
plt.show()
Notice that I have not added annotations displaying the coordinates of the points as in my experience, it requires a lot more code to position them nicely and have minimal overlapping. To get annotations, it is probably best to use the adjustText package or an interactive graphing library such as Plotly.