Line UM is the perpendicular bisector to line segment HK. The lines intersect at point J. If line segment HK measures 42 m, what is the measure of line segment JK?

Since line \( UM \) is the perpendicular bisector of line segment \( HK \), this means that it divides \( HK \) into two equal parts at the point of intersection, \( J \).

Given that the total length of \( HK \) is 42 meters, the two halves created by the perpendicular bisector are equal. So, the length of each half (i.e., \( JK \) and \( JH \)) will be:

\[
JK = \frac{HK}{2} = \frac{42}{2} = 21 \text{ meters}
\]

Thus, the length of line segment \( JK \) is **21 meters**.

Would you like further explanation or details on this? Here are 5 related questions to explore further:

1. What is the relationship between a perpendicular bisector and the angles it forms with the line it bisects?
2. How would the situation change if line \( UM \) was not perpendicular but still bisected \( HK \)?
3. How can we calculate the length of the bisected segments if \( UM \) was not given as the bisector?
4. Can we apply the Pythagorean theorem to find lengths of segments in this type of problem? If so, how?
5. How does the concept of congruent segments relate to this problem?

**Tip:** A perpendicular bisector always splits the line segment into two equal parts, and it forms a 90-degree angle with the segment it bisects.

Learn how to calculate the length of line segment JK when line UM is the perpendicular bisector of HK. This geometry problem involves understanding the perpendicular bisector theorem and dividing a line segment into equal parts. The total length of HK is 42 meters, and the length of JK is 21 meters. Suitable for students in Grades 6-8.

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