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

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Answer 1 · 2018-08-04T09:27:02

$C=(-1,-9)$

Explanation:

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

$• " a point "(x,y)to(y,-x)$

$A(2,1)toA'(1,-2)" where A' is the image of A"$

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

$ulb-ulc=2(ula'-ulc)$

$ulb-ulc=2ula'-2ulc$

$ulc=2ula'-ulb$

$color(white)(ulc)=2((1),(-2))-((3),(5))$

$color(white)(ulc)=((2),(-4))-((3),(5))=((-1),(-9))$

$rArrC=(-1,-9)$

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