For a real number $a$ with $\frac { 1 } { 4 } < a < 1$, let A and B be the points where the line $y = 1$ meets the curves $y = \log _ { a } x$ and $y = \log _ { 4 a } x$ respectively, and let C and D be the points where the line $y = - 1$ meets the curves $y = \log _ { a } x$ and $y = \log _ { 4 a } x$ respectively. Choose all correct statements from the following. [3 points]
$\langle$Statements$\rangle$
ㄱ. The point that divides segment AB externally in the ratio $1 : 4$ has coordinates $( 0,1 )$. ㄴ. If quadrilateral ABCD is a rectangle, then $a = \frac { 1 } { 2 }$. ㄷ. If $\overline { \mathrm { AB } } < \overline { \mathrm { CD } }$, then $\frac { 1 } { 2 } < a < 1$. (1) ㄱ (2) ㄷ (3) ㄱ, ㄴ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
For a real number $a$ with $\frac { 1 } { 4 } < a < 1$, let A and B be the points where the line $y = 1$ meets the curves $y = \log _ { a } x$ and $y = \log _ { 4 a } x$ respectively, and let C and D be the points where the line $y = - 1$ meets the curves $y = \log _ { a } x$ and $y = \log _ { 4 a } x$ respectively. Choose all correct statements from the following. [3 points]
\section*{$\langle$Statements$\rangle$}
ㄱ. The point that divides segment AB externally in the ratio $1 : 4$ has coordinates $( 0,1 )$.\\
ㄴ. If quadrilateral ABCD is a rectangle, then $a = \frac { 1 } { 2 }$.\\
ㄷ. If $\overline { \mathrm { AB } } < \overline { \mathrm { CD } }$, then $\frac { 1 } { 2 } < a < 1$.\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ