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)

Explanation:

Step1: Use the property of perpendicular bisector

Since \(JL\) is a perpendicular bisector of \(KM\), then \(KH = HM\).

Step2: Set up the equation

We know that \(KH=6y + 3\) and \(HM = 2y+7\). So, \(6y + 3=2y + 7\).

Step3: Solve the equation for \(y\)

Subtract \(2y\) from both sides: \(6y-2y+3=2y - 2y+7\), which gives \(4y+3 = 7\).
Subtract \(3\) from both sides: \(4y+3 - 3=7 - 3\), so \(4y=4\).
Divide both sides by \(4\): \(y=\frac{4}{4}=1\).

Step4: Find the length of \(HM\)

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

Answer:

\(9\)