Points A and B are at $(6 ,2 )$ and $(3 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ and dilated about point C by a factor of $2$ . 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 $(6 ,2 )$ and $(3 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-07-15T10:05:53

$color(indigo)("Coordinates of " C((x),(y)) = ((-11),(26))$

Explanation:

$A(9,7), B(3,8), "counterclockwise rotation "$ pi/2 $, "dilation factor" 2$

![https://teacher.desmos.com/activitybuilder/custom/566b16af914c731d06ef1953]( useruploads.socratic.org )

New coordinates of A after $(3pi)/2$ counterclockwise rotation

$A(9,7) rarr A' (-7,9)$

$vec (BC) = (2) vec(A'C)$

$b - c = (2)a' - (2)c$

$c = (2)a' - b$

$C((x),(y)) = (2)((-7),(9)) + ((3),(8)) = ((-11),(26))$

Answer 2 · 2018-07-15T11:22:17

$C=(-7,4)$

Explanation:

$"under a counterclockwise rotation about the origin of "pi/2$

$• " a point "(x,y)to(-y,x)$

$A(6,2)toA'(-2,6)" where A' is the image of A "$

$vec(CB)=color(red)(2)vec(CA')$

$ulb-ulc=2(ula'-ulc)$

$ulb-ulc=2ula'-2ulc$

$ulc=2ula'-ulb$

$color(white)(ulc)=2((-2),(6))-((3),(8))$

$color(white)(ulc)=((-4),(12))-((3),(8))=((-7),(4))$

$rArrC=(-7,4)$

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Points A and B are at $(6 ,2 )$ and $(3 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?

2 Answers

Explanation:

Explanation:

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Science

Math

Humanities

... and beyond

Points A and B are at (6 ,2 )(6 ,2 ) and (3 ,8 )(3 ,8 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 pi/2 and dilated about point C by a factor of 2 2 . If point A is now at point B, what are the coordinates of point C?

2 Answers

Explanation:

Explanation:

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Impact of this question

Points A and B are at $(6 ,2 )$ and $(3 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?