Question

1. using the diagram to the left, if line n bisects $overline{qr}$, find $qp$.

Explanation:

Step1: Set up the equation

Since line \(n\) bisects \(\overline{QR}\), then \(QP = PR\). So we set up the equation \(3x + 5=5x - 19\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(3x+5 - 3x=5x - 19-3x\), which simplifies to \(5 = 2x-19\). Then add 19 to both sides: \(5 + 19=2x-19 + 19\), getting \(24 = 2x\). Divide both sides by 2: \(\frac{24}{2}=\frac{2x}{2}\), so \(x = 12\).

Step3: Find \(QP\)

Substitute \(x = 12\) into the expression for \(QP\), \(QP=3x + 5\). Then \(QP=3\times12 + 5=36+5 = 41\).

Answer:

41