MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document Let P = ( 1 2 , 1 2 ) and Q = ( &#x2212; 1 2 , &#x2212; 1 2 ) be two vertices of a regular polygon having 12 sides such that PQ is a diameter of the circle circumscribing the polygon. Which of the following points is not a vertex of this polygon?(A) ( 3 &#x2212; 1 2 2 , 3 + 1 2 2 )(B) ( 3 + 1 2 2 , 3 &#x2212; 1 2 2 )(C) ( 3 + 1 2 2 , 1 &#x2212; 3 2 2 )(D) ( &#x2212; 1 2 , 3 2 )If P and Q are the end points of the diameter, it is quite clear that the equation of the circle must be

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MathJax(?): Can&#039;t find handler for document MathJax(?): Can&#039;t find handler for document Let   P  =  (      1          2        ,      1          2        ) and   Q  =  (  &amp;#x2212;      1          2        ,  &amp;#x2212;      1          2        ) be two vertices of a regular polygon having 12 sides such that PQ is a diameter of the circle circumscribing the polygon. Which of the following points is not a vertex of this polygon?(A)   (                    3            &amp;#x2212;      1              2              2              ,                    3            +      1              2              2              )(B)   (                    3            +      1              2              2              ,                    3            &amp;#x2212;      1              2              2              )(C)   (                    3            +      1              2              2              ,            1      &amp;#x2212;              3                    2              2              )(D)   (      &amp;#x2212;          1      2        ,            3        2    )If   P and   Q are the end points of the diameter, it is quite clear that the equation of the circle must be

Karla Hull · Accepted Answer

D) But how did I get that answer? Well, firstly have you drawn a picture of the diagram, with angles labelled? If so, then you’ll notice that the arg (angle from the x axis) of any point on the polygon must be 15 mod 30. The last option doesn’t satisfy this property (the angle it forms is 120 degrees).However, another approach is to notice — again from a well drawn diagram — that the figure is symmetric in the x axis, the y axis, and the x=y line. Since the first three options are just reflections of each other in these lines, the answer must be D. Meta analysis is useful in multiple choice!

Chant6j · Accepted Answer

MathJax(?): Can&#039;t find handler for document MathJax(?): Can&#039;t find handler for document A)

Let P = ( 1 <msqrt> 2 </msqrt> </mfrac> , 1 <msqrt>

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