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# whattt

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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. Mar 18, 2018

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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. Mar 19, 2018
edited by heureka  Mar 20, 2018