Suppose M is the midpoint of  FG⎯⎯⎯⎯⎯.
  Find the missing measure.

 

FM=5y+13,
   MG=5−3y

We are given that \( M \) is the midpoint of segment \( FG \), which means the distances \( FM \) and \( MG \) must be equal. We also know the following:

- \( FM = 5y + 13 \)
- \( MG = 5 - 3y \)

Since \( M \) is the midpoint, we set these two expressions equal to each other:

\[
5y + 13 = 5 - 3y
\]

Now, solve for \( y \):

1. Add \( 3y \) to both sides to combine like terms:
   \[
   5y + 3y + 13 = 5
   \]
   \[
   8y + 13 = 5
   \]

2. Subtract 13 from both sides:
   \[
   8y = 5 - 13
   \]
   \[
   8y = -8
   \]

3. Divide by 8:
   \[
   y = -1
   \]

Now that we have \( y = -1 \), substitute it back into either expression for \( FM \) or \( MG \) to find the length of each segment. Using \( FM = 5y + 13 \):

\[
FM = 5(-1) + 13 = -5 + 13 = 8
\]

Thus, both \( FM \) and \( MG \) are 8 units.

### Conclusion:
The missing measure is \( FM = MG = 8 \).

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Would you like more details on this solution? Here are some related questions:

1. How do you verify if a point is the midpoint of a segment?
2. What are the properties of midpoints in coordinate geometry?
3. Can you solve for the length of a segment if given different algebraic expressions?
4. How can midpoint calculations be used in real-life applications?
5. How would you solve a similar problem if the coordinates of points were given instead?

**Tip:** When solving equations with variables on both sides, always aim to simplify the equation step by step to isolate the variable.

Suppose M is the midpoint of FG. Find the missing measure.
FM=5y+13, MG=5−3y

Learn how to find the missing measure by solving the equation FM=5y+13 and MG=5−3y using the midpoint theorem. This problem explains how to equate two expressions and solve for y, suitable for students in Grades 7-9.

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