Points A and B are at $(6 ,1 )$ and $(3 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?

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Points A and B are at $(6 ,1 )$ and $(3 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-07-23T14:04:48

$C=(1/2,-35/4)$

Explanation:

$"under a counterclockwise rotation about the origin of "(3pi)/2$

$• " a point "(x,y)to(y,-x)$

$A(6,1)toA'(1,-6)" where A' is the image of A"$

$vec(CB)=color(red)(5)vec(CA')$

$ulb-ulc=5(ula'-ulc)$

$ulb-ulc=5ula'-5ulc$

$4ulc=5ula'-ulb$

$color(white)(4ulc)=5((1),(-6))-((3),(5))$

$color(white)(4ulc)=((5),(-30))-((3),(5))=((2),(-35))$

$ulc=1/4((2),(-35))=((1/2),(-35/4))$

$rArrC=(1/2,-35/4)$

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Points A and B are at $(6 ,1 )$ and $(3 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Humanities

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Points A and B are at (6 ,1 )(6 ,1 ) and (3 ,5 )(3 ,5 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 (3pi)/2 and dilated about point C by a factor of 5 5 . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Points A and B are at $(6 ,1 )$ and $(3 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?