Question:[br]The length of [math]\overline{AB}[/math] is 12, and [math]X[/math] is a variable point on [math]\overline{AB}[/math]. Squares [math]AXCD[/math] and [math]XBEF[/math] are drawn in a plane on the same side of [math]\overline{AB}[/math]. The centers of these squares are [math]Y[/math] and [math]Z[/math], respectively, and [math]W[/math] is the midpoint of [math]\overline{YZ}[/math]. As [math]X[/math] moves from [math]A[/math] to [math]B[/math], find the length of the path traced out by [math]W[/math].[br][br]Exploration:[br]Drag the point [math]X[/math] along [math]\overline{AB}[/math] to see the path traced out by [math]W[/math].