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 27 + 7 what is the length in units of segment HM

Answer 1

Since \( JL \) is the perpendicular bisector of \( KM \), it means that:

1. Point \( J \) is the midpoint of \( KM \).
2. The lengths from \( K \) to the midpoint \( J \) and from \( J \) to \( M \) are equal.

Therefore, we have:

\[ KH = HM \]

Given that \( KH = 6y + 3 \) and \( HM = 27 + 7 = 34 \), we set these equal to each other:

\[ 6y + 3 = 34 \]

Now, we will solve for \( y \):

1. Subtract 3 from both sides:

\[ 6y = 34 - 3 \] \[ 6y = 31 \]

2. Now, divide by 6:

\[ y = \frac{31}{6} \]

Even though we have found \( y \), we also need to find HM:

From the earlier equation for \( HM \):

\[ HM = 34 \text{ units} \]

Thus, the length of segment \( HM \) is:

\[ \boxed{34} \text{ units} \]