Is is possible to animate a point of a bezier curve? I am trying make a smooth transition from a line to an arrow.

Here's what the line looks like in code
//// Color Declarations
UIColor* white = [UIColor colorWithRed: 1 green: 1 blue: 1 alpha: 0.374];
//// Group
{
    //// Bezier Drawing
    UIBezierPath* bezierPath = [UIBezierPath bezierPath];
    [bezierPath moveToPoint: CGPointMake(30.5, 43.5)];
    [bezierPath addLineToPoint: CGPointMake(30.5, 29.59)];
    [bezierPath addLineToPoint: CGPointMake(30.5, 15.5)];
    bezierPath.lineCapStyle = kCGLineCapRound;
    bezierPath.lineJoinStyle = kCGLineJoinBevel;
    [white setStroke];
    bezierPath.lineWidth = 5.5;
    [bezierPath stroke];
}
... however I do not know how to pick a point and animate just that. Is this even possible?