Points A and B are at $(9, 3)$ $(9 ,3 )$ and $(7, 8)$ $(7 ,8 )$ , 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 $(9, 3)$ $(9 ,3 )$ and $(7, 8)$ $(7 ,8 )$ , 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 · 2018-06-27T10:28:42

$C = (- 25, - 14)$ $C=(-25,-14)$

Explanation:

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

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

$A(9,3)toA'(-9,-3)" where A' is the image of A"$

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

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

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

$ulc=2ula'-ulb$

$color(white)(ulc)=2((-9),(-3))-((7),(8))$

$color(white)(ulc)=((-18),(-6))-((7),(8))=((-25),(-14))$

$rArrC=(-25,-14)$

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Points A and B are at $(9, 3)$ $(9 ,3 )$ and $(7, 8)$ $(7 ,8 )$ , 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 ,3 )(9,3)(9 ,3 ) and (7 ,8 )(7,8)(7 ,8 ), 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 $(9, 3)$ $(9 ,3 )$ and $(7, 8)$ $(7 ,8 )$ , 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?