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 $3$ $3$ . 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 $(2, 7)$ $(2 ,7 )$ 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 $3$ $3$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-03-21T20:22:17

$C = (- 5, - \frac{27}{2})$ $C=(-5,-27/2)$

Explanation:

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

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

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

$rArrvec(CB)=color(red)(3)vec(CA')$

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

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

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((-2),(-7))-((4),(6))$

$color(white)(rArr2ulc)=((-6),(-21))-((4),(6))=((-10),(-27))$

$rArrulc=1/2((-10),(-27))=((-5),(-27/2))$

$rArrC=(-5,-27/2)$

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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 $3$ $3$ . 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 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 $(2, 7)$ $(2 ,7 )$ 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 $3$ $3$ . If point A is now at point B, what are the coordinates of point C?