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¯¯¯¯¯¯¯¯¯¯ ? (1 point) Responses 18 18 9 9 8 8 1

Answer 1

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

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

Next, we can solve for \( y \):

1. Subtract \( 2y \) from both sides:

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

2. Simplify:

\[ 4y + 3 = 7 \]

3. Subtract \( 3 \) from both sides:

\[ 4y = 4 \]

4. Divide 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 \( \boxed{9} \).