While reflecting a point about the $x$-axis, the magnitude of its $y$-coordinate remains the same but its sign changes. But the $x$-coordinate remains the same. This is because we are taking it to the quadrant below it. So, we can say that ${\text{R}}_{x}(x,y) = (x,-y)$.
While reflecting a point about the $y$-axis, the magnitude of its $x$-coordinate remains the same but its sign changes. But the $y$-coordinate remains the same. This is because we are taking it to the quadrant beside it. So, we can say that ${\text{R}}_{y}(x,y) = (-x,y)$.
While reflecting a point in the origin, the magnitude of its coordinates remains the same but their signs change. This is because we are taking it to the diagonally opposite quadrant. So, we can say ${\text{R}}_o (x,y) = (-x,-y)$.
Given that, $A(x,y) = A(-5,7)$
Now, $R_{y}\left(A(-5,7)\right) = B(5,7)$
$R_{x}\left(B(5,7)\right) = C(5,-7)$
$R_{o}\left(C(5,-7)\right) = D(-5,7)$
Here, we got $A(-5,7),$ and $D(-5,7)$ same.
$\therefore AD = 0.$
$\textbf{Short trick:}$
$P(x,y)\overset{R_{x}}{\longrightarrow} P(x,-y) \overset{R_{y}}{\longrightarrow} P(-x,-y)\overset{R_{o}}{\longrightarrow} P(x,y)$
$\textbf{Note:}$ The distance between two points $P= (x_1, y_1)$ and $Q = (x_2, y_2)$ can be found using the following formula:
$$PQ = \sqrt{(x_{1} - x_{2})^{2} + (y_{1}-y_{2})^{2}}$$
So, the correct answer is $0.$
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