JL¯¯¯¯¯¯¯JL¯ is a perpendicular bisector of KM¯¯¯¯¯¯¯¯¯¯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)

Question

9
18
1
8

Answer 1

Since \( JL \) is the perpendicular bisector of \( KM \), it means that point \( H \) is the midpoint of segment \( KM \). Therefore, the lengths \( KH \) and \( HM \) must be equal.

Given:

• Length of \( KH = 6y + 3 \)
• Length of \( HM = 2y + 7 \)

Since \( KH = HM \), we can set up the equation: \[ 6y + 3 = 2y + 7 \]

Now, let's solve for \( y \):

1. Subtract \( 2y \) from both sides: \[ 6y - 2y + 3 = 7 \] This simplifies to: \[ 4y + 3 = 7 \]

2. Subtract \( 3 \) from both sides: \[ 4y = 7 - 3 \] So, \[ 4y = 4 \]

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.