Points A and B are at $(9, 4)$ $(9 ,4 )$ and $(7, 2)$ $(7 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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 $(9, 4)$ $(9 ,4 )$ and $(7, 2)$ $(7 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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 · 2018-05-26T10:49:55

$C = (1, - 20)$ $C=(1,-20)$

Explanation:

$under a counterclockwise rotation about the origin of \frac{3 π}{2}$ $"under a counterclockwise rotation about the origin of "(3pi)/2$

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

$A(9,4)toA'(4,-9)" where A' is the image of A"$

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

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

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

$ulc=2ula'-ulb$

$color(white)(ulc)=2((4),(-9))-((7),(2))$

$color(white)(ulc)=((8),(-18))-((7),(2))=((1),(-20))$

$C=(1,-20)$

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Points A and B are at $(9, 4)$ $(9 ,4 )$ and $(7, 2)$ $(7 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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 ,4 )(9,4)(9 ,4 ) and (7 ,2 )(7,2)(7 ,2 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 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 $(9, 4)$ $(9 ,4 )$ and $(7, 2)$ $(7 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?