// Task 1

// Part 1
// unit_line_at : Number → Point

// Part 2
function vertical_line(pt, length){
    var x_new = x_of(pt);
    return function(t) {
        return make_point(x_new,
                          y_of(pt) + length * t);
    };
}

// Part 3
// vertical_line : (Point, Number) → Point

// Part 4
// (draw_connected(200))(vertical_line(make_point(0.5, 0.25), 0.5));

// Task 2
/*
Short answer: Symmetricity

Longer answer: The points start out dense and become thinner in
alternative_unit_circle while in unit_circle, they are evenly spaced.

From the implementation of the two functions, we have
x = sin(theta) and y = cos(theta), which is the parametric equation of a circle.

If we think of t as time, the pen moves in a circular path but with
different speed in the two cases.

In unit_circle, theta varies linearly to t (constant speed, physics stuff)
so the points are evenly spaced.

In alternative_unit_circle, theta is directly proportional to time squared,
which means the larger t gets, the faster the pen moves
(constant positive linear acceleration, physics stuff again).

Thus the increasingly sparse points in the alternative version.
*/