Question

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

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

Explanation:

Step1: Define mid - point property

Since line $n$ bisects $\overline{QR}$, then $QP = PR$. But we don't have enough info from the given part of the picture for $QP$ of $\overline{QR}$. For the second part about $\overline{XY}$, if $P$ is the mid - point of $\overline{XY}$, then $XP=PY$.

Step2: Set up equation

Set $8x - 2=12x - 30$.

Step3: Solve for $x$

$- 4x=-28$, so $x = 7$.

Answer:

$x = 7$