Points A and B are at $(2, 1)$ $(2 ,1 )$ and $(4, 7)$ $(4 ,7 )$ , 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 $(2, 1)$ $(2 ,1 )$ and $(4, 7)$ $(4 ,7 )$ , 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 · 2017-06-21T08:18:12

The coordinates of point $C = (- \frac{1}{2}, - \frac{13}{2})$ $C=(-1/2,-13/2)$

Explanation:

The matrix of a rotation counterclockwise by $\frac{3}{2} π$ $3/2pi$ about the origin is

$((0,1),(-1,0))$

Therefore, the transformation of point $A$ is

$A'=((0,1),(-1,0))((2),(1))=((1),(-2))$

Let point $C$ be $(x,y)$ , then

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

$((4-x),(7-y))=3((1-x),(-2-y))$

So,

$4-x=3(1-x)$

$4-x=3-3x$

$2x=-1$

$x=-1/2$

and

$7-y=3(-2-y)$

$7-y=-6-3y$

$2y=-6-7$

$y=-13/2$

Therefore,

point $C=(-1/2,-13/2)$

Answer 2 · 2017-06-21T08:32:26

$C=(-1/2,-13/2)$

Explanation:

$"under a counterclockwise rotation about the origin of " (3pi)/2$

$• " a point " (x,y)to(y,-x)$

$rArrA(2,1)toA'(1,-2)" where A' is the image of A"$

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

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

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

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

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((1),(-2))-((4),(7))$

$color(white)(rArr2ulc)=((3),(-6))-((4),(7))=((-1),(-13))$

$rArrulc=1/2((-1),(-13))=((-1/2),(-13/2))$

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

$rArrC=(-1/2,-13/2)$

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Points A and B are at $(2, 1)$ $(2 ,1 )$ and $(4, 7)$ $(4 ,7 )$ , 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?

2 Answers

Explanation:

Explanation:

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Points A and B are at (2 ,1 )(2,1)(2 ,1 ) and (4 ,7 )(4,7)(4 ,7 ), 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?

2 Answers

Explanation:

Explanation:

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Points A and B are at $(2, 1)$ $(2 ,1 )$ and $(4, 7)$ $(4 ,7 )$ , 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?