Points A and B are at $(1, 8)$ $(1 ,8 )$ and $(3, 6)$ $(3 ,6 )$ , 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 $(1, 8)$ $(1 ,8 )$ and $(3, 6)$ $(3 ,6 )$ , 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 · 2017-09-09T10:56:08

$C = (13, - 8)$ $C=(13,-8)$

Explanation:

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

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

$rArrA(1,8)toA'(8,-1)" where A' is the image of A"$

$"under a dilatation about C of factor 2"$

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

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

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((8),(-1))-((3),(6))$

$color(white)(rArrulc)=((16),(-2))-((3),(6))=((13),(-8))$

$rArrC=(13,-8)$

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Points A and B are at $(1, 8)$ $(1 ,8 )$ and $(3, 6)$ $(3 ,6 )$ , 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 (1 ,8 )(1,8)(1 ,8 ) and (3 ,6 )(3,6)(3 ,6 ), 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 $(1, 8)$ $(1 ,8 )$ and $(3, 6)$ $(3 ,6 )$ , 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?