Answer :
To find the point C, we need to use the formula for the midpoint:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Then the point C is:
[tex]C=(\frac{7+1}{2},\frac{2+(-2)}{2})=(\frac{8}{2},\frac{0}{2})=(4,0)[/tex]therefore, the point C is (4,0).
Now that we find the point C, we need to use the formula:
[tex]d(P,Q)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]to find the length of the segment AC:
[tex]\begin{gathered} d(A,C)=\sqrt[]{(4-1)^2+(0-(-2))^2} \\ =\sqrt[]{(3)^2+(2)^2} \\ =\sqrt[]{9+4} \\ =\sqrt[]{13} \\ =3.6 \end{gathered}[/tex]Therefore, the length of the segment AC is 13.