Points A and B are at $(8, 5)$ $(8 ,5 )$ and $(2, 2)$ $(2 ,2 )$ , 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 $3$ $3$ . 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 $(8, 5)$ $(8 ,5 )$ and $(2, 2)$ $(2 ,2 )$ , 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 $3$ $3$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-02-27T14:20:57

$C = (\frac{13}{2}, - 13)$ $C=(13/2,-13)$

Explanation:

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

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

$rArrA(8,5)toA'(5,-8)" where A' is the image of A"$

$rArrvec(CB)=color(red)(3)vec(CA')$

$rArrulb-ulc=3(ula'-ulc)$

$rArrulb-ulc=3ula'-3ulc$

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((5),(-8))-((2),(2))$

$color(white)(rArr2ulc)=((15),(-24))-((2),(2))=((13),(-26))$

$rArrulc=1/2((-13),(-26))=((13/2),(-13))$

$rArrC=(13/2,-13)$

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Points A and B are at $(8, 5)$ $(8 ,5 )$ and $(2, 2)$ $(2 ,2 )$ , 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 $3$ $3$ . 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 (8 ,5 )(8,5)(8 ,5 ) and (2 ,2 )(2,2)(2 ,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 3 33 . 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 $(8, 5)$ $(8 ,5 )$ and $(2, 2)$ $(2 ,2 )$ , 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 $3$ $3$ . If point A is now at point B, what are the coordinates of point C?