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# Defining a new example of a line L: ax + by + c = 0 a, b, c = 2, -1, 3 # Line equation 2x - y + 3 = 0 # Point P(x0, y0) for general reflection P0 = (4, 2) # Example point # Define the reflection formula using the generalized equation def reflection(P0, a, b, c): x0, y0 = P0 factor = 2 * (a * x0 + b * y0 + c) / (a**2 + b**2) x_prime = x0 - factor * a y_prime = y0 - factor * b return (x_prime, y_prime) # Compute P' P_prime_general = reflection(P0, a, b, c) # Line L equation in terms of y = (ax + c)/-b def L_general(x): return (a * x + c) / -b # Generate x values x_vals = np.linspace(-2, 8, 400) # Create the plot plt.figure(figsize=(8, 8)) plt.plot(x_vals, L_general(x_vals), label="Line L: $2x - y + 3 = 0$", color="blue") # Plot points P and P' plt.scatter(*P0, color="red", zorder=5, label="P(4, 2)") plt.scatter(*P_prime_general, color="purple", zorder=5, label="P'(image of P)") # Annotating the points plt.text(P0[0] + 0.2, P0[1], 'P(4, 2)', color="red") plt.text(P_prime_general[0] + 0.2, P_prime_general[1], "P'({:.2f}, {:.2f})".format(P_prime_general[0], P_prime_general[1]), color="purple") # Setting labels and title plt.axhline(0, color='black',linewidth=0.5) plt.axvline(0, color='black',linewidth=0.5) plt.xlabel('x') plt.ylabel('y') plt.title("Generalized Reflection of P(4, 2) over Line L: 2x - y + 3 = 0") plt.grid(True) plt.legend() plt.axis('equal') # Show the plot plt.show()
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