Points A and B are at $(2, 6)$ $(2 ,6 )$ and $(1, 9)$ $(1 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $\frac{1}{2}$ $1/2$ . 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 $(2, 6)$ $(2 ,6 )$ and $(1, 9)$ $(1 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $\frac{1}{2}$ $1/2$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-04-21T18:39:36

$C = (1, 6)$ $C=(1,6)$

Explanation:

$under a counterclockwise rotation about the origin of π$ $"under a counterclockwise rotation about the origin of "pi$

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

$rArrA(2,6)toA'(-2,-6)" where A' is the image of A"$

$rArrvec(CB)=color(red)(1/2)vec(CA')$

$rArrulb-ulc=1/2(ula'-ulc)$

$rArrulb-ulc=1/2ula'-1/2ulc$

$rArr1/2ulc=ulb-1/2ula'$

$color(white)(rArr1/2ulc)=((1),(9))-1/2((-2),(-6))$

$color(white)(rArr1/2ulc)=((1),(9))-((-1),(-3))=((2),(12))$

$rArrulc=1/2((2),(12))=((1),(6))$

$rArrC=(1,6)$

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Points A and B are at $(2, 6)$ $(2 ,6 )$ and $(1, 9)$ $(1 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $\frac{1}{2}$ $1/2$ . 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 ,6 )(2,6)(2 ,6 ) and (1 ,9 )(1,9)(1 ,9 ), respectively. Point A is rotated counterclockwise about the origin by pi πpi and dilated about point C by a factor of 1/2 121/2 . 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 $(2, 6)$ $(2 ,6 )$ and $(1, 9)$ $(1 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $\frac{1}{2}$ $1/2$ . If point A is now at point B, what are the coordinates of point C?