Points A and B are at $(9, 7)$ $(9 ,7 )$ and $(2, 5)$ $(2 ,5 )$ , 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 $3$ $3$ . 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 $(2, 5)$ $(2 ,5 )$ , 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 $3$ $3$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2017-07-09T10:51:18

$C = (- \frac{23}{2}, 11)$ $C=(-23/2,11)$

Explanation:

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

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

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

$"under a dilatation about C of factor 3"$

$vec(CB)=color(red)(3)vec(CA')$

$rArrulb-ulc=3ula'-3ulc$

. $rArr2ulc=3ula'-ulb$

$color(white)(rArr2)=3((-7),(9))-((2),(5))=((-21),(27))-((2),(5))$

$rArrulc=1/2((-23),(22))$

$color(white)(xxxx)=((-23/2),(11))$

$"the components of "ulc" are the coordinates of C"$

$rArrC=(-23/2,11)$

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Points A and B are at $(9, 7)$ $(9 ,7 )$ and $(2, 5)$ $(2 ,5 )$ , 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 $3$ $3$ . 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 (9 ,7 )(9,7)(9 ,7 ) and (2 ,5 )(2,5)(2 ,5 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 and dilated about point C by a factor of 3 33 . 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 $(2, 5)$ $(2 ,5 )$ , 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 $3$ $3$ . If point A is now at point B, what are the coordinates of point C?