https://file.aiquickdraw.com/mathbot/file/1727374188767hjyktcot.jpg

We are given that \( JL \) is a perpendicular bisector of \( KM \), and Hallie locates point \( H \) along the line segment \( JL \). The length of \( KH \) is given as \( 6y + 3 \), and the length of \( HM \) is given as \( 2y + 7 \). Since \( JL \) is a perpendicular bisector, the segments \( KH \) and \( HM \) should be equal.

### Steps to Solve:

1. Set the expressions for \( KH \) and \( HM \) equal to each other because they are bisected:
   \[
   6y + 3 = 2y + 7
   \]

2. Solve for \( y \):
   \[
   6y - 2y = 7 - 3
   \]
   \[
   4y = 4
   \]
   \[
   y = 1
   \]

3. Now, substitute \( y = 1 \) into the expression for \( HM \):
   \[
   HM = 2(1) + 7 = 2 + 7 = 9
   \]

Thus, the length of segment \( HM \) is **9 units**.

### Final Answer:
\[
\boxed{9}
\]

Would you like further details or have any questions?

Here are five related questions:
1. What is a perpendicular bisector, and how does it help in solving geometry problems?
2. How do you solve linear equations involving variables on both sides?
3. What are the properties of bisected line segments in a triangle?
4. How do you approach solving a word problem in geometry systematically?
5. Why is it important to check your solution by substituting values back into the original equations?

**Tip**: When solving geometry problems, visualizing or sketching the scenario can often make it easier to understand relationships between the elements!

JL is a perpendicular bisector of KM. Hallie locates point H along line segment JL. If the length of KH is given by 6y + 3 and the length of HM is given by 2y + 7, what is the length in units of segment HM?

Learn how to solve a problem involving a perpendicular bisector of KM, where lengths of segments are given by algebraic expressions. Find the length of HM using basic algebra and geometry. Suitable for students in Grades 7-10.

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