Question

point r is the mid - point of (overline{qs}), and (overline{qr}) is 19 inches long. what is the length of (overline{qs})?

Explanation:

Step1: Recall mid - point property

If a point \(M\) is the mid - point of a line segment \(\overline{AB}\), then \(AM = MB=\frac{1}{2}AB\). Here, point \(R\) is the mid - point of \(\overline{QS}\), so \(QR=\frac{1}{2}QS\).

Step2: Solve for \(QS\)

We know that \(QR = 19\) inches. Since \(QR=\frac{1}{2}QS\), then \(QS = 2\times QR\). Substituting \(QR = 19\) into the formula, we get \(QS=2\times19\).
\(QS = 38\)

Answer:

38