Question

learning target 4: i can apply the distance formula and segment addition postulate to find distances on a line. for questions 1-2, use the segment addition postulate. 1. use figure 1 to the right to find the measure of $overline{hj}$. 2. find the value of $c$ and $yz$ if $y$ is between $x$ and $z$. $xy = 11$, $yz = 4c$, $xz = 83$

Explanation:

Step1: Apply segment - addition postulate for question 1

The segment - addition postulate states that if J is between H and K, then \(HJ+JK = HK\). We know \(HK = 12.2\) ft and \(JK=3.1\) ft. So, \(HJ=HK - JK\).
\(HJ=12.2−3.1\)

Step2: Calculate the value of HJ

\(HJ = 9.1\) ft

Step3: Apply segment - addition postulate for question 2

Since Y is between X and Z, by the segment - addition postulate, \(XY + YZ=XZ\). We know \(XY = 11\), \(YZ = 4c\), and \(XZ = 83\). So, \(11+4c=83\).

Step4: Solve for c

Subtract 11 from both sides of the equation \(11 + 4c=83\):
\(4c=83 - 11\)
\(4c=72\)
Divide both sides by 4: \(c=\frac{72}{4}=18\)

Step5: Find the value of YZ

Since \(YZ = 4c\) and \(c = 18\), then \(YZ=4\times18 = 72\)

Answer:

1. \(HJ = 9.1\) ft
2. \(c = 18\), \(YZ = 72\)