8. If the line $2 x+y-2=0$ is perpendicular to the line $x+m y-1=0$, then the distance from point $P(m, m)$ to the line $x+y+3=0$ is

保留源文本的换行和格式，直接输出翻译结果。
Given that $2+m=0 \Rightarrow m=-2$, the distance from point $P(m, m)$ to the line $x+y+3=0$ is $d=\frac{|-2-2+3|}{\sqrt{2}}=\frac{\sqrt{2}}{2}$.