Update app.py

app.py

@@ -121,6 +121,9 @@ def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, U_x, U_y, G_x, G_y, midpoint
     # Plot midpoints of sides
     for i, (mx, my) in enumerate(midpoints):
         ax.scatter(mx, my, color=midpoint_color, zorder=5)
+    midpoints_labels = [f"Mid-Point M1 ({(x1 + x2) / 2:.3f}, {(y1 + y2) / 2:.3f})", 
+                        f"Mid-Point M2 ({(x2 + x3) / 2:.3f}, {(y2 + y3) / 2:.3f})", 
+                        f"Mid-Point M3 ({(x1 + x3) / 2:.3f}, {(y1 + y3) / 2:.3f})"]
 
     # Draw the inscribed circle (incircle)
     radius_in = calculate_radius_inscribed_circle(a, b, c)
@@ -137,9 +140,9 @@ def plot_triangle(x1, y1, x2, y2, x3, y3, I_x, I_y, U_x, U_y, G_x, G_y, midpoint
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[0]),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[1]),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=vertex_color, markersize=8, label=vertex_labels[2]),
-        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints[0]),
-        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints[1]),
-        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints[2]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints_labels[0]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints_labels[1]),
+        plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=midpoint_color, markersize=8, label=midpoints_labels[2]),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=incenter_color, markersize=8, label=key_points_labels[0]),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=circumcenter_color, markersize=8, label=key_points_labels[1]),
         plt.Line2D([0], [0], marker='o', color='w', markerfacecolor=centroid_color, markersize=8, label=key_points_labels[2])