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 8 8 9 9 1 1 18

Answer 1

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

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

To solve for \( y \), we first 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 we divide by \( 4 \):

\[ y = 1 \]

Now that we have the value of \( y \), we can find the length of segment \( HM \) using the expression \( HM = 2y + 7 \):

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

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