Perpendicular Bisector

Algebra Level 3

Consider the line segment whose endpoints are the \(x\)- and \(y\)-intercepts of \( 4 x + y -24 = 0 \), and let line \( l\) be the perpendicular bisector of this segment. If line \(l \) passes through \( (11,\ a) \), what is the value of \( a \) ?

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