In an equilateral triangle \( PQR \), let the vertex \( P \) be at \( (3, 5) \) and the side \( QR \) be along the line \( x + y = 4 \). If the orthocentre of the triangle \( PQR \) is \( (\alpha, \beta) \), then \( 9(\alpha + \beta) \) is equal to:
\( 16 \)
\( 27 \)
\( 36 \)
\( 48 \)
