*Segment PQ* is the perpendicular bisector of *Segmetn ST*. Find the values of m and *n.*

*Segment SP* = 3m + 9 *Segment SQ* = 6n -3

*Segment PT* = 5m - 13 *Segment TQ* = 4n + 14

(Only using your Answers just to make sure I'm correct.)

My Answer:

m=11 n=8.5

NiteWolf813
Jan 24, 2018

edited by
NiteWolf813
Jan 24, 2018

edited by NiteWolf813 Jan 24, 2018

edited by NiteWolf813 Jan 24, 2018

edited by NiteWolf813 Jan 24, 2018

edited by NiteWolf813 Jan 24, 2018

#1**+2 **

In this case, we can utilize the perpendicular bisector theorem, which states that \(\overline{SP}\cong\overline{PT}\). Therefore, set the measure of them equal to each other to figure out the unknown.

\(SP=PT\) | We know the length of these segments already. |

\(3m+9=5m-13\) | Subtract 2m from both sides first. |

\(9=2m-13\) | Add 13 to both sides. |

\(22=2m\) | Divide by 2 from both sides to isolate the variable completely. |

\(11=m\) | |

Using the same logic as before, we also know that \(\overline{SQ}\cong\overline{TQ}\).

\(SQ=TQ\) | Use substitution here! |

\(6n-3=4n+14\) | Subtract 4n from both sides. |

\(2n-3=14\) | Add 3 to both sides. |

\(2n=17\) | Divide by 2 from sides to isolate the unknown completely. This process is exactly the same as the first one. |

\(n=\frac{17}{2}=8.5\) | |

TheXSquaredFactor
Jan 24, 2018

#1**+2 **

Best Answer

In this case, we can utilize the perpendicular bisector theorem, which states that \(\overline{SP}\cong\overline{PT}\). Therefore, set the measure of them equal to each other to figure out the unknown.

\(SP=PT\) | We know the length of these segments already. |

\(3m+9=5m-13\) | Subtract 2m from both sides first. |

\(9=2m-13\) | Add 13 to both sides. |

\(22=2m\) | Divide by 2 from both sides to isolate the variable completely. |

\(11=m\) | |

Using the same logic as before, we also know that \(\overline{SQ}\cong\overline{TQ}\).

\(SQ=TQ\) | Use substitution here! |

\(6n-3=4n+14\) | Subtract 4n from both sides. |

\(2n-3=14\) | Add 3 to both sides. |

\(2n=17\) | Divide by 2 from sides to isolate the unknown completely. This process is exactly the same as the first one. |

\(n=\frac{17}{2}=8.5\) | |

TheXSquaredFactor
Jan 24, 2018