{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "LXlSRBeHtETj",
        "outputId": "6e624cf3-c557-409a-e729-d3050b8b36db"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Ejercicio Propuesto 2.2.4.\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def line_from_points(p1, p2):\n",
        "    \"\"\"Devuelve coeficientes (A,B,C) de la recta Ax + By + C = 0 que pasa por p1 y p2.\"\"\"\n",
        "    x1, y1 = p1\n",
        "    x2, y2 = p2\n",
        "    A = y1 - y2\n",
        "    B = x2 - x1\n",
        "    C = x1*y2 - x2*y1\n",
        "    return A, B, C\n",
        "\n",
        "def intersection(L1, L2):\n",
        "    \"\"\"Devuelve la intersección de dos rectas dadas por coeficientes (A,B,C).\"\"\"\n",
        "    A1, B1, C1 = L1\n",
        "    A2, B2, C2 = L2\n",
        "    det = A1*B2 - A2*B1\n",
        "    if det == 0:\n",
        "        return None  # Son paralelas\n",
        "    x = (B2*(-C1) - B1*(-C2)) / det\n",
        "    y = (A1*(-C2) - A2*(-C1)) / det\n",
        "    return (x, y)\n",
        "\n",
        "def ortocentro(A, B, C):\n",
        "    \"\"\"\n",
        "    Calcula el ortocentro de un triángulo con vértices A, B, C.\n",
        "    \"\"\"\n",
        "    # Recta BC\n",
        "    L_BC = line_from_points(B, C)\n",
        "    # Recta AC\n",
        "    L_AC = line_from_points(A, C)\n",
        "    # Recta AB\n",
        "    L_AB = line_from_points(A, B)\n",
        "\n",
        "    # Altura desde A -> perpendicular a BC que pasa por A\n",
        "    A1, B1, _ = L_BC\n",
        "    altura_A = (B1, -A1, -(B1*A[0] + -A1*A[1]))\n",
        "\n",
        "    # Altura desde B -> perpendicular a AC que pasa por B\n",
        "    A2, B2, _ = L_AC\n",
        "    altura_B = (B2, -A2, -(B2*B[0] + -A2*B[1]))\n",
        "\n",
        "    # Intersección de dos alturas\n",
        "    H = intersection(altura_A, altura_B)\n",
        "    return H, altura_A, altura_B\n",
        "\n",
        "# --- Ejemplo ---\n",
        "A = (1, 1)\n",
        "B = (7, 2)\n",
        "C = (3, 6)\n",
        "\n",
        "H, alt_A, alt_B = ortocentro(A, B, C)\n",
        "\n",
        "# --- Gráfica ---\n",
        "fig, ax = plt.subplots(figsize=(6,6))\n",
        "\n",
        "# Triángulo\n",
        "triangle_x = [A[0], B[0], C[0], A[0]]\n",
        "triangle_y = [A[1], B[1], C[1], A[1]]\n",
        "ax.plot(triangle_x, triangle_y, 'b-', lw=2, label='Triángulo')\n",
        "\n",
        "# Dibujar alturas\n",
        "def draw_line(line, x_range, style, label):\n",
        "    A, B, C = line\n",
        "    x_vals = np.linspace(x_range[0], x_range[1], 100)\n",
        "    y_vals = (-A*x_vals - C) / B\n",
        "    ax.plot(x_vals, y_vals, style, label=label)\n",
        "\n",
        "draw_line(alt_A, (0,8), 'r--', 'Altura desde A')\n",
        "draw_line(alt_B, (0,8), 'g--', 'Altura desde B')\n",
        "\n",
        "# Ortocentro\n",
        "ax.scatter(*H, color='purple', zorder=5, label='Ortocentro H')\n",
        "\n",
        "# Vértices\n",
        "for P, name in zip([A,B,C], ['A','B','C']):\n",
        "    ax.scatter(*P, color='black')\n",
        "    ax.text(P[0]+0.1, P[1]+0.1, name, fontsize=12)\n",
        "\n",
        "ax.set_aspect('equal')\n",
        "ax.grid(True)\n",
        "ax.legend()\n",
        "ax.set_title(\"Triángulo y su Ortocentro\")\n",
        "plt.show()"
      ]
    }
  ]
}