+0

whattt

0
57
1
+8

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.

ooojustwhy  Mar 18, 2018
Sort:

#1
+19207
+2

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.

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

25 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details