Question

given line l is the segment bisector of qr, find the
o 2x + 6 m 5x - 9 r

Explanation:

Step1: Use mid - point property

Since line \(l\) is the segment bisector of \(QR\), then \(QM = MR\). So, \(2x + 6=5x - 9\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(6 = 5x-2x - 9\), which simplifies to \(6 = 3x - 9\). Then add 9 to both sides: \(6 + 9=3x\), so \(15 = 3x\). Divide both sides by 3, we get \(x = 5\).

Step3: Find \(QM\) or \(MR\)

Substitute \(x = 5\) into the expression for \(QM\) (we could also use the expression for \(MR\)). \(QM=2x + 6=2\times5+6=10 + 6=16\).

Step4: Find \(QR\)

Since \(QR=QM + MR\) and \(QM = MR = 16\), then \(QR=16+16 = 32\).

Answer:

32