As shown in the figure, let $\mathrm { A }$ and $\mathrm { B }$ be the $x$-intercept and $y$-intercept, respectively, of the graph of the function $y = \frac { k } { x - 1 } + 3$ where $0 < k < 3$. [Figure] Let $\mathrm { P }$ be the point (other than $\mathrm { B }$) where the line passing through the intersection of the two asymptotes of this graph and point $\mathrm { B }$ meets the graph, and let $\mathrm { Q }$ be the foot of the perpendicular from point $\mathrm { P }$ to the $x$-axis. Which of the following statements are correct? [4 points] ㄱ. When $k = 1$, the coordinates of point $\mathrm { P }$ are $( 2,4 )$. ㄴ. For real numbers $0 < k < 3$, the sum of the slope of line AB and the slope of line AP is 0. ㄷ. When the area of quadrilateral PBAQ is a natural number, the slope of line BP is between 0 and 1. (1) ㄱ (2) ㄱ, ㄴ (3) ㄱ, ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
As shown in the figure, let $\mathrm { A }$ and $\mathrm { B }$ be the $x$-intercept and $y$-intercept, respectively, of the graph of the function $y = \frac { k } { x - 1 } + 3$ where $0 < k < 3$.\\
\includegraphics[max width=\textwidth, alt={}, center]{26f53191-c2e9-4115-98d0-f3837666a14d-08_515_592_571_1204}\\
Let $\mathrm { P }$ be the point (other than $\mathrm { B }$) where the line passing through the intersection of the two asymptotes of this graph and point $\mathrm { B }$ meets the graph, and let $\mathrm { Q }$ be the foot of the perpendicular from point $\mathrm { P }$ to the $x$-axis. Which of the following statements are correct? [4 points]\\
ㄱ. When $k = 1$, the coordinates of point $\mathrm { P }$ are $( 2,4 )$.\\
ㄴ. For real numbers $0 < k < 3$, the sum of the slope of line AB and the slope of line AP is 0.\\
ㄷ. When the area of quadrilateral PBAQ is a natural number, the slope of line BP is between 0 and 1.\\
(1) ㄱ\\
(2) ㄱ, ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ