Points A and B are at $(6 ,1 )$ and $(8 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2017-05-28T07:06:26

The point $C=(-20,-11)$

A rotation counterclockwise by $pi$ , point $A$ becomes $A'$

$A=(6,1)$

The coordinates of $A'=(-6,-1)$

Let the point $C=(x,y)$

So,

$vec(CB)=2vec(CA')$

$((8-x),(9-y))=2((-6-x),(-1-y))$

Therefore,

$8-x=-12-2x$ , $=>$ , $x=-12-8=-20$

$9-y=-2-2y$ , $=>$ , $y=-2-9=-11$

The point $C=(-20,-11)$

Points A and B are at (6 ,1 )(6 ,1 ) and (8 ,9 )(8 ,9 ), respectively. Point A is rotated counterclockwise about the origin by pi pi and dilated about point C by a factor of 2 2 . If point A is now at point B, what are the coordinates of point C?