Points A and B are at $(9, 7)$ $(9 ,7 )$ and $(8, 6)$ $(8 ,6 )$ , 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 $(9, 7)$ $(9 ,7 )$ and $(8, 6)$ $(8 ,6 )$ , 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 · 2018-06-22T10:25:09

$C = (- 26, - 20)$ $C=(-26,-20)$

Explanation:

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

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

$A(9,7)toA'(-9,-7)" where A' is the image of A"$

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

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

$ulb-ulc=2ula'-2ulc$

$ulc=2ula'-ulb$

$color(white)(ulc)=2((-9),(-7))-((8),(6))$

$color(white)(ulc)=((-18),(-14))-((8),(6))=((-26),(-20))$

$rArrC=(-26,-20)$

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Points A and B are at $(9, 7)$ $(9 ,7 )$ and $(8, 6)$ $(8 ,6 )$ , 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 (9 ,7 )(9,7)(9 ,7 ) and (8 ,6 )(8,6)(8 ,6 ), 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 $(9, 7)$ $(9 ,7 )$ and $(8, 6)$ $(8 ,6 )$ , 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?