Python (Length input to draw star with a center point of 0,0)
Question: I have some code were the users input the length they want their star to be
and then it draws out the star. What I am trying to accomplish here, is that
every-time they make their input not only that it draws the star but it also
keeps it centered in the screen. so middle point 0,0

    
    
    import turtle
    
    Length = eval(input("enter the length you want for your star: "))
    
    turtle.penup()
    turtle.goto(0,200)
    turtle.pendown()
    turtle.goto(0,-200)
    turtle.penup()
    turtle.goto(200,0)
    turtle.pendown()
    turtle.goto(-200,0)
    
    turtle.penup()
    turtle.goto(0,0)
    
    turtle.showturtle
    turtle.pendown()
    turtle.left(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    


Answer: Try this

    
    
    import turtle
    import math
    
    theta = 18  * math.pi / 180   # convert degrees to radians
    
    Length = eval(input("enter the length you want for your star: "))
    
    x = math.sin(theta) * Length
    y = math.cos(theta)* Length / 2
    
    turtle.penup()
    turtle.goto(0,200)
    turtle.pendown()
    turtle.goto(0,-200)
    turtle.penup()
    turtle.goto(200,0)
    turtle.pendown()
    turtle.goto(-200,0)
    
    turtle.penup()
    #turtle.goto(0,0)
    turtle.goto(x,-y)
    
    turtle.showturtle
    turtle.pendown()
    turtle.left(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.right(36*4)
    turtle.forward(Length)
    turtle.hideturtle()
    
    input("Press Enter to exit")
    

It's just a matter of figuring out the coordinates of the center of the star
you were drawing, and then translating the starting position by that vector,
to move the center to the origin.

EDIT:

If you go back to your original drawing, to the left of the y-axis, your see
two line segments, in an inverted V-shape. If we join the two intersections of
these segments with the x-axis to each other, we have an isosceles triangle
whose center is the center of the star. That's the point we need to find. Now,
each angle of the star is 36 degrees, and half that is 18. That's where the 18
comes from. To actually find the center, we need to use some trigonometry,
which I gather you haven't studied yet. The functions sin and cos are the sine
and cosine functions from trigonometry. The arguments to these functions are
usually given not in degrees, but in another system called radians. It happens
that 1800 degrees is the same as pi radians, so theta is just an 18 degree
angle, measured in radians.

"Why 18 degrees," did I hear you ask? Remember that we're try to find the
center of that isosceles triangle, with two side equal to length, and a
hypotenuse of Length. So, we I drop a perpendicular to the base, we cut it
into two right triangles, with one acute angle of 18 degrees (and the other 72
degrees.) And this is where the sine and cosine come in. In a right triangle
with hypotenuse Length, the side opposite an acute angle theta has length
`sin(theta)*Length` and the side adjacent to the angle theta has length
`cos(theta)*Length`.

This is a long-winded explanation, but I don't know how to make it shorter in
this format. You can find an explanation with pictures
[here](https://www.mathsisfun.com/algebra/trigonometry.html)

