Let $\Gamma$ be the function graph of $y = \sin \pi x$ for $0 \leq x \leq 3$. A horizontal line $L : y = k$ intersects $\Gamma$ at three points $P \left( x _ { 1 } , k \right) , Q \left( x _ { 2 } , k \right) , R \left( x _ { 3 } , k \right)$ satisfying $x _ { 1 } < x _ { 2 } < 1 < x _ { 3 }$. Select the correct options. (1) $k > 0$ (2) $L$ and $\Gamma$ have exactly 3 intersection points (3) $x _ { 1 } + x _ { 2 } < 1$ (4) If $2 \overline { P Q } = \overline { Q R }$, then $k = \frac { 1 } { 2 }$ (5) The sum of $x$-coordinates of all intersection points of $L$ and $\Gamma$ is greater than 5
Let $\Gamma$ be the function graph of $y = \sin \pi x$ for $0 \leq x \leq 3$. A horizontal line $L : y = k$ intersects $\Gamma$ at three points $P \left( x _ { 1 } , k \right) , Q \left( x _ { 2 } , k \right) , R \left( x _ { 3 } , k \right)$ satisfying $x _ { 1 } < x _ { 2 } < 1 < x _ { 3 }$. Select the correct options.\\
(1) $k > 0$\\
(2) $L$ and $\Gamma$ have exactly 3 intersection points\\
(3) $x _ { 1 } + x _ { 2 } < 1$\\
(4) If $2 \overline { P Q } = \overline { Q R }$, then $k = \frac { 1 } { 2 }$\\
(5) The sum of $x$-coordinates of all intersection points of $L$ and $\Gamma$ is greater than 5