Points A and B are at $(9 ,4 )$ and $(1 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $3$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2017-08-12T11:57:03

The coordinates of $C=(11/2,-16)$

Point $A=((9),(4))$ and point $B=((1),(5))$

The rotation of point $A$ counterclockwise by $(3/2pi)$ tranforms the point $A$ into

$A'=((4),(-9))$

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

The dilatation is

$vec(CB)=3vec(CA')$

$((1),(5))-((x),(y))=3*((4),(-9))-((x),(y)))$

Therefore,

$1-x=3(4-x)$

$1-x=12-3x$

$2x=12-1=11$ , $=>$ , $x=11/2$

$5-y=3(-9-y)$

$5-y=-27-3y$

$2y=-27-5=-32$ , $=>$ , $y=-16$

The point $C=(11/2,-16)$

Points A and B are at (9 ,4 )(9 ,4 ) and (1 ,5 )(1 ,5 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 (3pi)/2 and dilated about point C by a factor of 3 3 . If point A is now at point B, what are the coordinates of point C?