+10 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
+2441 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. |
| \(n=\frac{17}{2}=8.5\) | |
+2441 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. |
| \(n=\frac{17}{2}=8.5\) | |
