[tex]a)\ \ AB^2=(x_B-x_A)^2+(y_B-y_A)^2=(5+3)^2+(7-13)^2=\\ \\ =64+36=100=10^2\Rightarrow AB=10\\ \\ \\ b)\ \ a-3=\dfrac{x_A+x_B}{2} \Rightarrow a-3=\dfrac{-3+5}{2}=\dfrac{2}{2}=1 \Rightarrow a=4\\ \\ 3b+1=\dfrac{y_A+y_B}{2}=\dfrac{13+7}{2}=10 \Rightarrow b=3[/tex]
