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

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Answer 1 · 2018-07-15T10:12:18

$color(maroon)("Coordinates of point C " (-9/2, -1/2)$

Explanation:

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

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

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

$A(2,2) rarr A' (-2,2)$

$vec (BC) = (3) vec(A'C)$

$b - c = (3)a' - (3)c$

$2c = (3)a' - b$

$c = (3/2)a' -(1/2) b$

$C((x),(y)) = (3/2)((-2),(2)) - (1/2) ((3),(7)) = ((-9/2),(-1/2))$

Answer 2 · 2018-07-15T10:33:38

$C=(-9/2,-1/2)$

Explanation:

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

$• " a point "(x,y)to(-y,x)$

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

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

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

$ulb-ulc=3ula'-3ulc$

$2ulc=3ula'-ulb$

$color(white)(2ulc)=3((-2),(2))-((3),(7))$

$color(white)(2ulc)=((-6),(6))-((3),(7))=((-9),(-1))$

$ulc=1/2((-9),(-1))=((-9/2),(-1/2))$

$rArrC=(-9/2,-1/2)$

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Points A and B are at $(2 ,2 )$ and $(3 ,7 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ and dilated about point C by a factor of $3$ . 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

Science

Math

Humanities

... and beyond

Points A and B are at (2 ,2 )(2 ,2 ) and (3 ,7 )(3 ,7 ), respectively. Point A is rotated counterclockwise about the origin by pi/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?

2 Answers

Explanation:

Explanation:

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Impact of this question

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