Question

proofs about angles quick check
$overline{jl}$ is a perpendicular bisector of $overline{km}$. halle locates point $h$ along line segment $overline{jl}$. if the length of $overline{kh}$ is given by $6y + 3$ and the length of $overline{hm}$ is given by $2y+7$, what is the length in units of segment $overline{hm}$? (1 point)
9
18
1
8

Explanation:

Step1: Use property of perpendicular bisector

Since $\overline{JL}$ is a perpendicular bisector of $\overline{KM}$, then $KH = HM$. So we set up the equation $6y + 3=2y + 7$.

Step2: Solve for $y$

Subtract $2y$ from both sides: $6y-2y + 3=2y-2y + 7$, which simplifies to $4y+3 = 7$. Then subtract 3 from both sides: $4y+3 - 3=7 - 3$, getting $4y=4$. Divide both sides by 4: $y = 1$.

Step3: Find length of $HM$

Substitute $y = 1$ into the expression for $HM$. $HM=2y + 7$. So $HM=2\times1+7=9$.

Answer:

9