Question

if ( overline{vy} cong overline{xy} ), ( vw = 2p ), and ( wx = p + 28 ), what is the value of ( p )?

Explanation:

Step1: Use the perpendicular bisector theorem

Since \( \overline{VY}\cong\overline{XY}\) and \( WY\perp VX\), by the perpendicular bisector theorem, \( VW = WX\).

Step2: Set up the equation

We know \( VW = 2p\) and \( WX=p + 28\). Substitute into \( VW = WX\), we get \(2p=p + 28\).

Step3: Solve the equation

Subtract \(p\) from both sides of the equation \(2p=p + 28\).
\(2p-p=p + 28-p\)
\(p = 28\)

Answer:

\(28\)