Question

consider the diagram. what is qs? 2 units. 5 units. 17 units. 33 units.

Explanation:

Step1: Use the perpendicular bisector theorem

Since \(l\) is the perpendicular bisector of \(RQ\), by the perpendicular bisector theorem, \(RS = QS\). So, \(3x + 2=5x - 8\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(2 = 2x-8\).
Add \(8\) to both sides: \(2 + 8=2x\), so \(10 = 2x\).
Divide both sides by \(2\): \(x = 5\).

Step3: Find the length of \(QS\)

Substitute \(x = 5\) into the expression for \(QS\) (\(QS=5x - 8\)).
\(QS=5\times5 - 8=25 - 8 = 17\)

Answer:

17 units.