7. Let the moving points be $P(t, 0), Q(1, t)(t \in[0,1])$. Then the area of the plane region swept by the line segment $P Q$ is $\qquad$ .
7. $\frac{1}{6}$.

Let $l_{P Q}: y=\frac{t}{1-t}(x-t)$.
Fix $x \in[0,1]$, as $t$ varies in the interval $[0, x]$,
$$
y=2-x-\left(\frac{1-x}{1-t}+1-t\right)
$$

the range of values is $0 \leqslant y \leqslant 2-x-2 \sqrt{1-x}$. 
Therefore, the area of the desired planar region is
$$
\int_{0}^{1}(2-x-2 \sqrt{1-x}) \mathrm{d} x=\frac{1}{6} \text {. }
$$