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

8
8

1
1

18
18

9

Answer 1

Since \( JL \) is the perpendicular bisector of \( KM \), we have:

\[
KH = HM
\]

Given the expressions for the lengths:

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

Setting these two expressions equal to each other since \( KH = HM \):

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

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

1. Subtract \( 2y \) from both sides:
\[
4y + 3 = 7
\]

2. Subtract 3 from both sides:
\[
4y = 4
\]

3. Divide both sides by 4:
\[
y = 1
\]

Now substitute \( y = 1 \) back into the expression for \( HM \):

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

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