Points A and B are at $(3, 5)$ $(3 ,5 )$ and $(6, 1)$ $(6 ,1 )$ , 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 $(3, 5)$ $(3 ,5 )$ and $(6, 1)$ $(6 ,1 )$ , 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 · 2018-03-21T13:54:43

$C = (- \frac{21}{2}, 4)$ $C=(-21/2,4)$

Explanation:

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

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

$rArrA(3,5)toA'(-5,3)" where A' is the image of A"$

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

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

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

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((-5),(3))-((6),(1))$

$color(white)(rArr2ulc)=((-15),(9))-((6),(1))=((-21),(8))$

$rArrulc=1/2((-21),(8))=((-21/2),(4))$

$rArrC=(-21/2,4)$

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Points A and B are at $(3, 5)$ $(3 ,5 )$ and $(6, 1)$ $(6 ,1 )$ , 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 (3 ,5 )(3,5)(3 ,5 ) and (6 ,1 )(6,1)(6 ,1 ), 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 $(3, 5)$ $(3 ,5 )$ and $(6, 1)$ $(6 ,1 )$ , 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?