Question

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

Explanation:

Step1: Recall mid - point property

Since $P$ is the mid - point of $\overline{XY}$, then $XP = PY$.

Step2: Set up the equation

Set $8x−2=12x - 30$.

Step3: Solve for $x$

First, move the $x$ terms to one side:
$12x-8x=30 - 2$.
$4x=28$.
Then divide both sides by 4:
$x=\frac{28}{4}=7$.

Answer:

$7$