Question

qr = 3 units
what is the length of tq, the image of segment tq?
tq = units

Explanation:

Step1: Analyze the original segment lengths

We can observe from the graph that \(QR = 1\) unit and \(QT=2\) units.

Step2: Determine the scale factor

Since \(QR' = 3\) units and \(QR = 1\) unit, the scale factor \(k=\frac{QR'}{QR}=\frac{3}{1} = 3\).

Step3: Calculate the length of \(T'Q\)

We know that if a segment is dilated with scale factor \(k\), the length of the image of a segment \(l'\) is related to the length of the original segment \(l\) by the formula \(l'=k\times l\).
For segment \(TQ\) with length \(l = QT= 2\) units and scale factor \(k = 3\), then \(T'Q=k\times QT\).
Substitute \(k = 3\) and \(QT = 2\) into the formula: \(T'Q=3\times2\).

Answer:

\(6\)