Mathematics

Grade Levels: 6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade,

Topics: Algebra

Common Core State Standard: G-GPE.7,

Knowledge and Skills:

· Can interpret (x,y,z) notation as the position of a point in three-dimensional space

· Can find the distance between two points in three-dimensional space

Lesson:

Procedure: This project should be done by students individually or teams of two.

Distribute the handout and ensure that students understand the task.

**Answers:**

(x1,y1,z1) |
(x2,y2,z2) |
Distance |

(3,5,8) | (4,10,14) | 8 |

(4,9,1) | (7,0,12) | 15 |

(18,3,22) | (5,12,19) | 16 |

(-4,12,35) | (14,7,50) | 24 |

(-12,6,-15) | (-16,-2,0) | 17 |

(25,-50,25) | (-25,50,-25) | 122 |

(2.25,5.45,9.15) | (3.15,8.75,7.95) | 3.62 |

(15.36,24.17,18.72) | (22.78,12.39,32.18) | 19.36 |

(128,94,276) | (253,146,275) | 135 |

(265,4,74) | (4,265,74) | 369 |

(-340,25,212) | (-120,-202,0) | 381 |

(1005,2144,1546) | (1010,2150,1550) | 9 |

**The Distance Between Two Points**

**Skill Set**

(x1, y1,z1) and (x2,y2,z2) represent the coordinates of two points in threedimensional space, in meters. Find the distance between the two points in each case. (Round the computed distances to the lowest decimal place that occurs in the coordinates.)

(x1,y1,z1) |
(x2,y2,z2) |
Distance |

(3,5,8) | (4,10,14) | |

(4,9,1) | (7,0,12) | |

(18,3,22) | (5,12,19) | |

(-4,12,35) | (14,7,50) | |

(-12,6,-15) | (-16,-2,0) | |

(25,-50,25) | (-25,50,-25) | |

(2.25,5.45,9.15) | (3.15,8.75,7.95) | |

(15.36,24.17,18.72) | (22.78,12.39,32.18) | |

(128,94,276) | (253,146,275) | |

(265,4,74) | (4,265,74) | |

(-340,25,212) | (-120,-202,0) | |

(1005,2144,1546) | (1010,2150,1550) |