Given the two points P(-5,4) and Q(7,-5), we can find the length of the line PQ with the general formula for the distance between two points:
[tex]\begin{gathered} P(─5,4) \\ Q(7,─5) \\ d(P,Q)=\sqrt[]{(x_2─x_1)^2+(y_2─y_1)^2} \\ \Rightarrow d(P,Q)=\sqrt[]{(7─(─5))^2+(─5─4)^2}=\sqrt[]{(7+5)^2+(─9)^2} \\ =\sqrt[]{(12)^2+81}=\sqrt[]{144+81}=\sqrt[]{225}=15 \\ d(P,Q)=15 \end{gathered}[/tex]therefore, the length of PQ is 15 units
