Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]then, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(3,4)=A \\ (x_2,y_2)=(-1,10)=B \\ \Rightarrow d(A,B)=\sqrt[]{(-1-3)^2+(10-4)^2}=\sqrt[]{4^2+6^2}=\sqrt[]{16+36}=\sqrt[]{52} \\ =\sqrt[]{4\cdot13}=2\cdot\sqrt[]{13} \\ d(A,B)=2\cdot\sqrt[]{13} \end{gathered}[/tex]