Points A and B are at $(2, 7)$ $(2 ,7 )$ and $(4, 6)$ $(4 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $4$ $4$ . 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 $(2, 7)$ $(2 ,7 )$ and $(4, 6)$ $(4 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $4$ $4$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-02-27T10:50:52

$C = (- 4, - \frac{34}{3})$ $C=(-4,-34/3)$

Explanation:

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

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

$rArrA(2,7)toA'(-2,-7)" where A' is the image of A"$

$rArrvec(CB)=color(red)(4)vec(CA')$

$rArrulb-ulc=4(ula'-ulc)$

$rArrulb-ulc=4ula'-4ulc$

$rArr3ulc=4ula'-ulb$

$color(white)(rArr3ulc)=4((-2),(-7))-((4),(6))$

$color(white)(rArr3ulc)=((-8),(-28))-((4),(6))=((-12),(-34))$

$rArrulc=1/3((-12),(-34))=((-4),(-34/3))$

$rArrC=(-4,-34/3)$

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Points A and B are at $(2, 7)$ $(2 ,7 )$ and $(4, 6)$ $(4 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $4$ $4$ . 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 (2 ,7 )(2,7)(2 ,7 ) and (4 ,6 )(4,6)(4 ,6 ), respectively. Point A is rotated counterclockwise about the origin by pi πpi and dilated about point C by a factor of 4 44 . 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 $(2, 7)$ $(2 ,7 )$ and $(4, 6)$ $(4 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ and dilated about point C by a factor of $4$ $4$ . If point A is now at point B, what are the coordinates of point C?