Question

review problems

1. line segment pk is the perpendicular bisector of $overline{rn}$, where $rp = 9x - 5.1$ and $pn = 6x + 1.2$, as shown. find the value of x.

Explanation:

Step1: Recall Perpendicular Bisector Property

Since \( PK \) is the perpendicular bisector of \( \overline{RN} \), by the perpendicular bisector theorem, \( RP = PN \).

Step2: Set Up the Equation

Set \( 9x - 5.1 = 6x + 1.2 \).

Step3: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 9x - 6x - 5.1 = 1.2 \), which simplifies to \( 3x - 5.1 = 1.2 \).
Add \( 5.1 \) to both sides: \( 3x = 1.2 + 5.1 \), so \( 3x = 6.3 \).
Divide both sides by \( 3 \): \( x = \frac{6.3}{3} = 2.1 \).

Answer:

\( x = 2.1 \)