***

дано:

[tex]\displaystyle \bf B(1; -5)[/tex]

[tex]\diplaystyle \bf C(-1; 2)[/tex]

______

[tex]\displaystyle \bf A(x_1 \ y_1) = \ ?[/tex]

решение:

[tex]\displaystyle \bf X_2=1\ \ \ \ \ \ \ \ \ \ X=-1\\\ Y_2=-5 \ \ \ \ \ \ \ \ Y=2[/tex]

[tex]\displaystyle \bf X=\frac{X_1+X_2}{2} \ \ \ \ \ \ \ \ \ \ \ Y=\frac{Y_1+Y_2}{2} \\\\\\-1=\frac{X_1+1}{2} \ \ \ \ \ \ \ \ \ \ \ \ 2=\frac{Y_1-5}{2} \\\\\\X_1+1=-1\cdot 2 \ \ \ \ \ \ \ \ \ \ Y_1-5=2\cdot 2\\\\\\X_1=-2-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ Y_1=4-(-5)=4+5=9\\\\\\\boxed{\Big \displaystyle X_1=-3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{ \Big \displaystyle Y_1=9}[/tex]        

ответ: A(-3; 9)