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

Answer 1

Since \( JL \) is the perpendicular bisector of segment \( KM \), it implies that \( KH \) is equal to \( HM \). Thus, we can set the two expressions for the lengths of \( KH \) and \( HM \) equal to each other:

\[ KH = HM \]

Substituting the given expressions:

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

Now, to solve for \( y \), we will first subtract \( 2y \) from both sides:

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

This simplifies to:

\[ 4y + 3 = 7 \]

Next, we will subtract 3 from both sides:

\[ 4y = 4 \]

Now, divide both sides by 4:

\[ y = 1 \]

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

\[ HM = 2y + 7 \]

Substituting \( y = 1 \):

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

Thus, the length of segment \( HM \) is \( \boxed{9} \) units.