Answer
10
Work Step by Step
Use the distance formula to find the length of $\overline{AB}$.
$d_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$
substitute
$d_{AB}=\sqrt{(3-(-4))^2+(5-5)^2}$
$d_{AB}=\sqrt{(7)^2+(0)^2}$
$d_{AB}=\sqrt{49+0}$
$d_{AB}=\sqrt{49}$
$d_{AB}=7$
Since the y-coordinate of A and B are the same, $\overline{AB}$ is a horizontal line. If B is the midpoint of $\overline{AC}$ then A, B and C are collinear and $\overline{AC}$ is also a horizontal line with a y-coordinate of 5.
If B is the midpoint of $\overline{AC}$, the length of $\overline{AC}$ is twice the length of $\overline{AB}$.
$AC=2(AB)=2(7)=14$
Use the distance formula to find the x-coordinate of point C.
$d_{AC}=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}$
substitute
$14=\sqrt{(x_C-(-4))^2+(5-5)^2}$
$14=\sqrt{(x_C+4)^2+(0)^2}$
$14=\sqrt{(x_C+4)^2}$
$14=x_C+4$
subtract 4 from each side
$14-4=x_C+4-4$
$10=x_C$
