Question

review problems 4. 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

A perpendicular bisector of a segment implies the two segments from the point on the bisector to the endpoints are equal. So \( RP = PN \).
\( 9x - 5.1 = 6x + 1.2 \)

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 9x - 6x - 5.1 = 1.2 \)
Simplify: \( 3x - 5.1 = 1.2 \)
Add \( 5.1 \) to both sides: \( 3x = 1.2 + 5.1 \)
Calculate: \( 3x = 6.3 \)
Divide by 3: \( x = \frac{6.3}{3} \)
\( x = 2.1 \)

Answer:

\( x = 2.1 \)