Question

1. if p is the mid - point of $overline{xy}$, $xp = 8x - 2$ and $py = 12x - 30$, find the value of x.

Explanation:

Step1: Use mid - point property

Since \(P\) is the mid - point of \(\overline{XY}\), then \(XP = PY\). So we set up the equation \(8x - 2=12x - 30\).

Step2: Solve the equation for \(x\)

First, move the \(x\) terms to one side: \(12x-8x = 30 - 2\).
Combining like terms gives \(4x=28\).
Then divide both sides by 4: \(x=\frac{28}{4}\).

Answer:

\(x = 7\)