Points A and B are at $(1, 5)$ $(1 ,5 )$ and $(2, 3)$ $(2 ,3 )$ , 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 $4$ $4$ . 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 $(1, 5)$ $(1 ,5 )$ and $(2, 3)$ $(2 ,3 )$ , 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 $4$ $4$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-03-14T14:11:28

$C = (6, \frac{1}{3})$ $C=(6,1/3)$

Explanation:

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

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

$rArrA(1,5)toA'(5,1)" where A' is the image of A"$

$rArrvec(CB)=color(red)(4)vec(CA')$

$rArrulb-ulc=4(ula'-ulc)$

$rArrulb-ulc=4ula'-4ulc$

$rArr3ulc=4ula'-ulb$

$color(white)(rArr3ulc)=4((5),(1))-((2),(3))$

$color(white)(rArr3ulc)=((20),(4))-((2),(3))=((18),(1))$

$rArrulc=1/3((18),(1))=((6),(1/3))$

$rArrC=(6,1/3)$

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Points A and B are at $(1, 5)$ $(1 ,5 )$ and $(2, 3)$ $(2 ,3 )$ , 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 $4$ $4$ . 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 ,5 )(1,5)(1 ,5 ) and (2 ,3 )(2,3)(2 ,3 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 and dilated about point C by a factor of 4 44 . 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 $(1, 5)$ $(1 ,5 )$ and $(2, 3)$ $(2 ,3 )$ , 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 $4$ $4$ . If point A is now at point B, what are the coordinates of point C?