Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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 $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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 · 2018-05-11T13:31:36

$C = (- 10, - 16)$ $C=(-10,-16)$

Explanation:

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

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

$rArrA(3,7)toA'(-3,-7)" where A' is the image of A"$

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

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

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

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((-3),(-7))-((4),(2))$

$color(white)(rArrulc)=((-6),(-14))-((4),(2))=((-10),(-16))$

$rArrC=(-10,-16)$

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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 (3 ,7 )(3,7)(3 ,7 ) and (4 ,2 )(4,2)(4 ,2 ), respectively. Point A is rotated counterclockwise about the origin by pi πpi 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 $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?