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In rectangle ABCD, P is the center point of DC. Q is a moving point on AB (doesn't overlap with A or B).

If the length of AQ is x and the sum of QM and QN is y,

choose the graph below that best describes the relationship between x and y.

$\text{Let $\angle A =\angle\ PAB = \angle\ PBA $ } \\ \text{Let $AQ = x $ } \\ \text{Let $QM + QN = y $ }$

$\begin{array}{|rcl|rcl|} \hline \sin(A) &=& \dfrac{QM}{x} & \sin(A) &=& \dfrac{QN}{AB-x} \\ \hline \end{array} \\ \begin{array}{|rcll|} \hline y(x) &=& QM + QN \\ &=& x \sin(A) + (AB-x) \sin(A) \\ &=& \sin(A) ( x + AB-x) \\ &=& AB\sin(A) \quad & \quad \text{y is constant} \\ \hline \end{array}$

D.