Question

Points A and B are at `(8 ,5 )` and `(2 ,2 )`, 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=(13/2,-13)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(8,5)toA'(5,-8)" 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((5),(-8))-((2),(2))`

`color(white)(rArr2ulc)=((15),(-24))-((2),(2))=((13),(-26))`

`rArrulc=1/2((-13),(-26))=((13/2),(-13))`

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