Points A and B are at $(2, 4)$ $(2 ,4 )$ and $(3, 5)$ $(3 ,5 )$ , 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 $(2, 4)$ $(2 ,4 )$ and $(3, 5)$ $(3 ,5 )$ , 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 · 2018-02-02T19:50:24

$C = (- 11, - 1)$ $C=(-11,-1)$

Explanation:

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

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

$rArrA(2,4)toA'(-4,2)" where A' is the image of A"$

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

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

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

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((-4),(2))-((3),(5))$

$color(white)(rArrulc)=((-8),(4))-((3),(5))=((-11),(-1))$

$rArrC=(-11,-1)$

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Points A and B are at $(2, 4)$ $(2 ,4 )$ and $(3, 5)$ $(3 ,5 )$ , 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?

1 Answer

Explanation:

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Points A and B are at (2 ,4 )(2,4)(2 ,4 ) and (3 ,5 )(3,5)(3 ,5 ), 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 $(2, 4)$ $(2 ,4 )$ and $(3, 5)$ $(3 ,5 )$ , 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?