I am having a problem finding a point at a specific distance between 2 points. Suppose I have point A(1,1) and point B(4,4). I know the distance between these 2 points is 4.24. However, I do not know how to find point C, which is 1/4 the distance from point A to point B. How do I find point C?

What you are looking for is the midpoint - http://en.wikipedia.org/wiki/Midpoint

I am having a problem finding a point at a specific distance between 2 points. Suppose I have point A(1,1) and point B(4,4). I know the distance between these 2 points is 4.24. However, I do not know how to find point C, which is 1/4 the distance from point A to point B. How do I find point C?

to find a line 1/4th of the distance between 2 points you just need:

Vector2D p1(1,1);
Vector2D p2(4,4);

Vector2D direction = p2-p1

Vector2D p3 = p1+ direction* 0.25; (assuming your vector library supports scalar multiplication, if not its simply p3.x = p1.x + direction.x*0.25 and same for y)

If you don't have a vector library you can simply do

p1x=1;
p1y=1;
p2x=4;
p2y=4;

dirx=p2x-p1x;
diry=p2y-p1y;

p3x = p1x+dirx*0.25;
p3y = p1y+diry*0.25;

Using vector algebra:
C = (B - A) * .25 + A
C = (<4,4> - <1,1>) * .25 + <1,1>
C = <3,3> * .25 + <1,1>
C = <.75,.75> + <1,1>
C = <1.75, 1.75>

Or:
Cx = (Bx - Ax) * .25 + Ax
Cy = (By - Ay) * .25 + Ay

thank you very much!!