Question

1. if p is the mid - point of xy, xp = 8x - 2, and py = 12x - 30, find the value of x. 10. if g is the mid - point of fh, fg = 14x + 25, and gh = 73 - 2x, find fh. 11. using the diagram to the left, if line n bisects qr, find qp.

Explanation:

Step1: Use mid - point property

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: \(5 = 2x-19\). Then add 19 to both sides: \(24 = 2x\). Divide both sides by 2, we get \(x = 12\).

Step3: Find \(QP\)

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

Answer:

\(41\)