Suppose M is the midpoint of  JK⎯⎯⎯⎯⎯
 ,  JM=12a+2
 , and  JK=76
 . Find a.

 

a = 

To find the value of \( a \), we need to use the fact that \( M \) is the midpoint of line segment \( JK \). This means that \( JM = MK \), and both \( JM \) and \( MK \) are half of \( JK \).

Given:
- \( JM = 12a + 2 \)
- \( JK = 76 \)

Since \( M \) is the midpoint, the length of \( JM \) is half of \( JK \):
\[
JM = \frac{JK}{2}
\]

Substitute the given values:
\[
12a + 2 = \frac{76}{2}
\]

Calculate the right side:
\[
12a + 2 = 38
\]

Now, solve for \( a \):

1. Subtract 2 from both sides:
   \[
   12a = 38 - 2
   \]
   \[
   12a = 36
   \]

2. Divide both sides by 12:
   \[
   a = \frac{36}{12}
   \]
   \[
   a = 3
   \]

So, the value of \( a \) is \( \boxed{3} \).

Would you like more details on this solution or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the significance of a midpoint in geometry?
2. How would you find the midpoint of a line segment on a coordinate plane?
3. If \( M \) is the midpoint of another line segment \( PQ \) with \( PQ = 100 \), what would \( PM \) be?
4. What is the formula for the distance between two points in coordinate geometry?
5. How do you find the length of a line segment if you know the coordinates of its endpoints?

**Tip:** When solving geometry problems involving midpoints, always remember that the midpoint divides the line segment into two equal parts.

Suppose M is the midpoint of JK⎯⎯⎯⎯⎯, JM=12a+2, and JK=76. Find a.

Learn how to find the value of 'a' when given the midpoint of a line segment JK, with JM=12a+2 and JK=76. This problem involves understanding midpoints in geometry and solving linear equations, suitable for students in Grades 6-8.

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