Parametric Path on a Polygonal Path

Your task it to change [math]x(t)[/math] and [math]x(t)[/math] so the [color=#1551b5][b]BLUE[/b][/color] point will move from the [color=#0a971e][b]starting point[/b][/color] to the [color=#c51414][b]stopping point[/b][/color] along the polygonal path through point D when you drag the [color=#b20ea8][b]slider t[/b][/color].