Question

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

8
8

1
1

9

Answer 1

Since \( JL \) is a perpendicular bisector of \( KM \), it means that \( KH \) is equal to \( HM \).

Given:

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

Setting these equal to each other since they are equal lengths:

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

Now, let's 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 by 4:
\[
y = 1
\]

Now, substituting \( y \) back in to find the length of \( HM \):

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

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