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)

Answer 1

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

We can set up the equation based on the given lengths:

\[ KH = HM \]

Substituting the expressions provided:

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

To solve for \(y\), we first isolate the \(y\) terms. Begin by subtracting \(2y\) from both sides:

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

This simplifies to:

\[ 4y + 3 = 7 \]

Next, subtract 3 from both sides:

\[ 4y = 4 \]

Now, divide by 4:

\[ y = 1 \]

Now, we need to find the length of segment \(HM\). We can use the expression for \(HM\) and substitute \(y = 1\):

\[ HM = 2y + 7 \]

Substituting \(y\):

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

Thus, the length of segment \(HM\) is:

\[ \boxed{9} \] units.