Question

for exercises 5 - 7, use the figure shown. 5. what is pq? 6. what is qr? 7. what is pr? 3. st = 3 4. ru = 12

Explanation:

Step1: Identify segment - length relationships

We know that on a line - segment, if we have points \(P\), \(Q\), \(R\) such that \(P\), \(Q\), \(R\) are collinear, and we are given the positions of the points on the number - line. The length of a line - segment with endpoints \(a\) and \(b\) (\(a\lt b\)) is \(b - a\).

Step2: Calculate \(PQ\)

The coordinate of \(P\) is \(3\) and the coordinate of \(Q\) is \(8\). So \(PQ=8 - 3\).
\[PQ = 5\]

Step3: Calculate \(QR\)

The coordinate of \(Q\) is \(8\) and the coordinate of \(R\) is \(14\). So \(QR=14 - 8\).
\[QR = 6\]

Step4: Calculate \(PR\)

The coordinate of \(P\) is \(3\) and the coordinate of \(R\) is \(14\). So \(PR=14 - 3\).
\[PR = 11\]

Answer:

1. \(PQ = 5\)
2. \(QR = 6\)
3. \(PR = 11\)