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)

Question

GPT-4o mini · Answer

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:

$K H = H M$

Substituting the expressions provided:

$6 y + 3 = 2 y + 7$

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

$6 y - 2 y + 3 = 7$

This simplifies to:

$4 y + 3 = 7$

Next, subtract 3 from both sides:

$4 y = 4$

Now, divide by 4:

$y = 1$

Now, we need to find the length of segment $H M$ . We can use the expression for $H M$ and substitute $y = 1$ :

$H M = 2 y + 7$

Substituting $y$ :

$H M = 2 (1) + 7 = 2 + 7 = 9$

Thus, the length of segment $H M$ is:

$9$ units.