Question

point p is on line segment \overline{oq}. given oq = 2x, op = x, and pq = 10, determine the numerical length of \overline{oq}.

Explanation:

Step1: Use the segment addition postulate

Since \(P\) is on \(\overline{OQ}\), we have \(OQ = OP+PQ\).
Substituting the given values: \(2x=x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(2x=x + 10\).
\(2x-x=x + 10-x\), which gives \(x = 10\).

Step3: Find the length of \(OQ\)

We know that \(OQ=2x\). Substitute \(x = 10\) into the formula.
\(OQ=2\times10\).

Answer:

\(20\)