Points A and B are at $(7, 3)$ $(7 ,3 )$ and $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Points A and B are at $(7, 3)$ $(7 ,3 )$ and $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Answer 1 · 2018-05-18T14:56:59

$C = (3, - 16)$ $C=(3,-16)$

Explanation:

$under a counterclockwise rotation about the origin of \frac{3 π}{2}$ $"under a counterclockwise rotation about the origin of "(3pi)/2$

$∙ a point (x, y) \to (y, - x)$ $• " a point "(x,y)to(y,-x)$

$rArrA(7,3)toA'(3,-7)" where A' is the image of A"$

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

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

$rArrulb-ulc=2ula'-2ulc$

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((3),(-7))-((3),(2))$

$color(white)(rArrulc)=((6),(-14))-((3),(2))=((3),(-16))$

$rArrC=(3,-16)$

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Points A and B are at $(7, 3)$ $(7 ,3 )$ and $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Explanation:

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Points A and B are at (7 ,3 )(7,3)(7 ,3 ) and (3 ,2 )(3,2)(3 ,2 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 and dilated about point C by a factor of 2 22 . 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 $(7, 3)$ $(7 ,3 )$ and $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?