Points A and B are at $(8, 2)$ $(8 ,2 )$ and $(3, 7)$ $(3 ,7 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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 $(8, 2)$ $(8 ,2 )$ and $(3, 7)$ $(3 ,7 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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 · 2018-02-26T14:25:50

$C = (- \frac{9}{2}, \frac{17}{2})$ $C=(-9/2,17/2)$

Explanation:

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

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

$rArrA(8,2)toA'(-2,8)" where A' is the image of A"$

$rArrvec(CB)-color(red)(3)vec(CA')$

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

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

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((-2),(8))-((3),(7))$

$color(white)(rArr2ulc)=((-6),(24))-((3),(7))=((-9),(17))$

$rArrulc=1/2((-9),(17))=((-9/2),(17/2))$

$rArrC=(-9/2,17/2)$

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Points A and B are at $(8, 2)$ $(8 ,2 )$ and $(3, 7)$ $(3 ,7 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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 (8 ,2 )(8,2)(8 ,2 ) and (3 ,7 )(3,7)(3 ,7 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 π2pi/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 $(8, 2)$ $(8 ,2 )$ and $(3, 7)$ $(3 ,7 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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?