Points A and B are at $(6, 1)$ $(6 ,1 )$ and $(8, 9)$ $(8 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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 $(6, 1)$ $(6 ,1 )$ and $(8, 9)$ $(8 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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 · 2017-10-04T08:03:37

$C = (- 13, - 6)$ $C=(-13,-6)$

Explanation:

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

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

$rArrA(6,1)toA'(-6,-1)" where A' is the image of A"$

$"under a dilatation about C of factor 3"$

$vec(CB)=3vec(CA')$

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

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

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((-6),(-1))-((8),(9))$

$color(white)(rArrulc)=((-18),(-3))-((8),(9))=((-26),(-12))$

$rArrulc=1/2((-26),(-12))=((-13),(-6))$

$rArrC=(-13,-6)$

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Points A and B are at $(6, 1)$ $(6 ,1 )$ and $(8, 9)$ $(8 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

1 Answer

Explanation:

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Points A and B are at (6 ,1 )(6,1)(6 ,1 ) and (8 ,9 )(8,9)(8 ,9 ), respectively. Point A is rotated counterclockwise about the origin by pi πpi 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 $(6, 1)$ $(6 ,1 )$ and $(8, 9)$ $(8 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?