Example 2. On a line segment $AB$ of length 1, take two points $C, D$ in the order of $A, B, C, D$. Let $AC=x$, $CD=y$.
(1) Draw a diagram to represent the range of point $P(x, y)$.
(2) If the segments $AC, CD, DB$ can form the sides of a triangle, draw a diagram to represent the range of point $P(x, y)$.
$$
\begin{array}{l}
\text { (1) A, B, C, and D are four distinct points arranged in sequence, } x>0, y>1, x+y 1 - ( x + y ) , } \\
{ x + 1 - ( x + y ) > y , } \\
{ y + 1 - ( x + y ) > x , }
\end{array} \text { that is } \left\{\begin{array}{l}
x+y>\frac{1}{2}, \\
0<x<\frac{1}{2} \\
0<y<\frac{1}{2} .
\end{array}\right.\right.
$$

The required range is the interior of $\triangle G H K$ (Figure 2).
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