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 \( KH = HM \). We can set up the equation based on the information provided about the lengths \( KH \) and \( HM \):

\[ KH = HM \]

We know:

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

Setting them equal to each other gives us the equation:

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

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

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

\[ 6y - 2y + 3 = 7 \ 4y + 3 = 7 \]

2. Subtract 3 from both sides:

\[ 4y = 4 \]

3. Divide both sides by 4:

\[ y = 1 \]

Now we can find the length of segment \( HM \):

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

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