Question

Points A and B are at `(2 ,9 )` and `(8 ,7 )`, respectively. Point A is rotated counterclockwise about the origin by `(3pi)/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?

Answer 1

`C=(19/2,-13/2)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(2,9)toA'(9,-2)" 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((9),(-2))-((8),(7))`

`color(white)(rArr2ulc)=((27),(-6))-((8),(7))=((19),(-13))`

`rArrulc=1/2((19),(-13))=((19/2),(-13/2))`

`rArrC=(19/2,-13/2)`