Question

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

Answer 1

Since line segment JL is the perpendicular bisector of line segment KM, point H must be the midpoint of segment KM. Therefore, the lengths of segments KH and HM must be equal.

Given:

- \( KH = 6y + 3 \)
- \( HM = 2y + 7 \)

Since \( KH = HM \), we can set the two expressions equal to each other:

\[
6y + 3 = 2y + 7
\]

Next, we will solve for \( y \). First, we subtract \( 2y \) from both sides:

\[
6y - 2y + 3 = 7
\]

This simplifies to:

\[
4y + 3 = 7
\]

Next, we subtract 3 from both sides:

\[
4y = 4
\]

Now, divide both sides by 4:

\[
y = 1
\]

Now that we have the value of \( y \), we can find the length of segment \( HM \):

Substituting \( y = 1 \) into the expression for \( HM \):

\[
HM = 2y + 7 = 2(1) + 7 = 2 + 7 = 9
\]

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

\[
\boxed{9} \text{ units}
\]