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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

off-topic
 Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018

Best Answer 

 #1
avatar+2338 
+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.
\(n=\frac{17}{2}=8.5\)  
   
 Jan 24, 2018
 #1
avatar+2338 
+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

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