Calculate the area and centroid of a triangle with vertices at (1,2), (3,4), and (5,6)

Area = | |x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) + x_{3}(y_{1} - y_{2})| |

2 |

Area = | |1(4 - 6) + 3(6 - 2) + 5(2 - 4)| |

2 |

Area = | |1(-2) + 3(4) + 5(-2)| |

2 |

Area = | |-2 + 12 + -10| |

2 |

Area = | |0| |

2 |

Area =

x_{1} + x_{2} + x_{3} | |

3 |

, |

y_{1} + y_{2} + y_{3} |

3 |

1 + 3 + 5 | |

3 |

, |

2 + 4 + 6 |

3 |

9 | |

3 |

, |

12 |

3 |

Centroid = (