Question

Points A and B are at `(6 ,1 )` and `(3 ,5 )`, 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=(1/2,-35/4)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`A(6,1)toA'(1,-6)" where A' is the image of A"`

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

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

`ulb-ulc=5ula'-5ulc`

`4ulc=5ula'-ulb`

`color(white)(4ulc)=5((1),(-6))-((3),(5))`

`color(white)(4ulc)=((5),(-30))-((3),(5))=((2),(-35))`

`ulc=1/4((2),(-35))=((1/2),(-35/4))`

`rArrC=(1/2,-35/4)`