Points A and B are at $(1, 7)$ $(1 ,7 )$ and $(3, 9)$ $(3 ,9 )$ , 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 $5$ $5$ . 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 $(1, 7)$ $(1 ,7 )$ and $(3, 9)$ $(3 ,9 )$ , 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 $5$ $5$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-05-01T14:49:59

$C = (8, - \frac{7}{2})$ $C=(8,-7/2)$

Explanation:

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

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

$rArrA(1,7)toA'(7,-1)" where A' is the image of A"$

$rArrvec(CB)=color(red)(5)vec(CA')$

$rArrulb-ulc=5(ula'-ulc)$

$rArrulb-ulc=5ula'-5ulc$

$rArr4ulc=5ula'-ulb$

$color(white)(rArr4ulc)=5((7),(-1))-((3),(9))$

$color(white)(rArr4ulc)=((35),(-5))-((3),(9))=((32),(-14))$

$rArrulc=1/4((32),(-14))=((8),(-7/2))$

$rArrC=(8,-7/2)$

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Points A and B are at $(1, 7)$ $(1 ,7 )$ and $(3, 9)$ $(3 ,9 )$ , 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 $5$ $5$ . 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 (1 ,7 )(1,7)(1 ,7 ) and (3 ,9 )(3,9)(3 ,9 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 and dilated about point C by a factor of 5 55 . 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 $(1, 7)$ $(1 ,7 )$ and $(3, 9)$ $(3 ,9 )$ , 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 $5$ $5$ . If point A is now at point B, what are the coordinates of point C?