As shown in the figure, $L$ is a line passing through the origin $O$ on the coordinate plane, $\Gamma$ is a circle centered at $O$, and $L$ and $\Gamma$ have one intersection point $A ( 3,4 )$. It is known that $B , C$ are two distinct points on $\Gamma$ satisfying $\overrightarrow { B C } = \overrightarrow { O A }$. Select the correct options. (1) The other intersection point of $L$ and $\Gamma$ is $( - 4 , - 3 )$ (2) The slope of line $B C$ is $\frac { 3 } { 4 }$ (3) $\angle A O C = 60 ^ { \circ }$ (4) The area of $\triangle A B C$ is $\frac { 25 \sqrt { 3 } } { 2 }$ (5) $B$ and $C$ are in the same quadrant
As shown in the figure, $L$ is a line passing through the origin $O$ on the coordinate plane, $\Gamma$ is a circle centered at $O$, and $L$ and $\Gamma$ have one intersection point $A ( 3,4 )$. It is known that $B , C$ are two distinct points on $\Gamma$ satisfying $\overrightarrow { B C } = \overrightarrow { O A }$. Select the correct options.\\
(1) The other intersection point of $L$ and $\Gamma$ is $( - 4 , - 3 )$\\
(2) The slope of line $B C$ is $\frac { 3 } { 4 }$\\
(3) $\angle A O C = 60 ^ { \circ }$\\
(4) The area of $\triangle A B C$ is $\frac { 25 \sqrt { 3 } } { 2 }$\\
(5) $B$ and $C$ are in the same quadrant