On the coordinate plane, there is a square and a regular hexagon, with the square to the right of the hexagon. Both regular polygons have one side on the $x$-axis, and the center $A$ of the square and the center $B$ of the hexagon are both above the $x$-axis. The two polygons have exactly one intersection point $P$. The side length of the square is 6, and the distance from point $P$ to the $x$-axis is $2\sqrt{3}$. Select the correct options. (1) The distance from point $A$ to the $x$-axis is greater than the distance from point $B$ to the $x$-axis (2) The side length of the regular hexagon is 6 (3) $\overrightarrow{BA} = (7, 3 - 2\sqrt{3})$ (4) $\overline{AP} > \sqrt{10}$ (5) The slope of line $AP$ is greater than $-\frac{1}{\sqrt{3}}$
On the coordinate plane, there is a square and a regular hexagon, with the square to the right of the hexagon. Both regular polygons have one side on the $x$-axis, and the center $A$ of the square and the center $B$ of the hexagon are both above the $x$-axis. The two polygons have exactly one intersection point $P$. The side length of the square is 6, and the distance from point $P$ to the $x$-axis is $2\sqrt{3}$. Select the correct options.\\
(1) The distance from point $A$ to the $x$-axis is greater than the distance from point $B$ to the $x$-axis\\
(2) The side length of the regular hexagon is 6\\
(3) $\overrightarrow{BA} = (7, 3 - 2\sqrt{3})$\\
(4) $\overline{AP} > \sqrt{10}$\\
(5) The slope of line $AP$ is greater than $-\frac{1}{\sqrt{3}}$