Question

in the diagram, \\( \overline { t q } \\) is 18 units in length. what is the length of \\( \overline { r s } \\)? 16 units 18 units 25 units 46 units

Explanation:

Step1: Use the property of perpendicular bisector

Since line \(l\) is the perpendicular bisector of \(RQ\), \(RS = QS\). So \(2x + 10=9x - 11\).

Step2: Solve the equation for \(x\)

$$
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$$

Step3: Find the length of \(RQ\)

Since \(TQ = 18\) and \(T\) is the mid - point of \(RQ\) (because \(l\) is the perpendicular bisector), \(RQ=2\times TQ = 36\). And \(RT=TQ = 18\).

Step4: Calculate the length of \(RS\)

Substitute \(x = 3\) into \(RS=2x + 10\). Then \(RS=2\times3+10=16\)

Answer:

16 units