Points A and B are at $(1, 8)$ $(1 ,8 )$ and $(3, 2)$ $(3 ,2 )$ , 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 $2$ $2$ . If point A is now at point B, what are the coordinates of point C?

Question

Points A and B are at $(1, 8)$ $(1 ,8 )$ and $(3, 2)$ $(3 ,2 )$ , 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 $2$ $2$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Impact of this question

1170 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-26T10:07:56

$C = (13, - 4)$ $C=(13,-4)$

Explanation:

$under a counterclockwise rotation about the origin of \frac{3 π}{2}$ $"under a counterclockwise rotation about the origin of "(3pi)/2$

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

$rArrA(1,8)toA'(8,-1)" where "A'" is the image of A"$

$"under a dilatation about C of factor 2"$

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

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

$rArrulb-ulc=2ula'-2ulc$

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((8),(-1))-((3),(2))$

$color(white)(rArrulc)=((16),(-2))-((3),(2))=((13),(-4))$

$rArrC=(13,-4)$

Science

Math

Humanities

... and beyond

Points A and B are at $(1, 8)$ $(1 ,8 )$ and $(3, 2)$ $(3 ,2 )$ , 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 $2$ $2$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Points A and B are at (1 ,8 )(1,8)(1 ,8 ) and (3 ,2 )(3,2)(3 ,2 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 and dilated about point C by a factor of 2 22 . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

Related questions

Impact of this question

Points A and B are at $(1, 8)$ $(1 ,8 )$ and $(3, 2)$ $(3 ,2 )$ , 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 $2$ $2$ . If point A is now at point B, what are the coordinates of point C?