Question

Points A and B are at `(1 ,7 )` and `(3 ,9 )`, respectively. Point A is rotated counterclockwise about the origin by `(3pi)/2` and dilated about point C by a factor of `5`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(8,-7/2)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(1,7)toA'(7,-1)" where A' is the image of A"`

`rArrvec(CB)=color(red)(5)vec(CA')`

`rArrulb-ulc=5(ula'-ulc)`

`rArrulb-ulc=5ula'-5ulc`

`rArr4ulc=5ula'-ulb`

`color(white)(rArr4ulc)=5((7),(-1))-((3),(9))`

`color(white)(rArr4ulc)=((35),(-5))-((3),(9))=((32),(-14))`

`rArrulc=1/4((32),(-14))=((8),(-7/2))`

`rArrC=(8,-7/2)`