To answer this question we will use the following formula to compute the distance between two given points (x,y) and (v,w):
[tex]d=\sqrt{(x-v)^2+(y-w)^2}.[/tex]
From the given diagram we get that:
[tex]\begin{gathered} P=(-5,-1), \\ Q=(1,-4). \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} PQ=\sqrt{(-5-1)^2+(-1-(-4))^2}=\sqrt{(-6)^2+(3)^2} \\ \sqrt{36+9}=\sqrt{45}\approx6.71. \end{gathered}[/tex]
Answer:
[tex]6.71.[/tex]
