Question

Points A and B are at `(4 ,5 )` and `(6 ,8 )`, respectively. Point A is rotated counterclockwise about the origin by `(3pi)/2` and dilated about point C by a factor of `4`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(14/3,-8)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`A(4,5)toA'(5,-4)" where A' is the image of A"`

`vec(CB)=color(red)(4)vec(CA')`

`ulb-ulc=4(ula'-ulc)`

`ulb-ulc=4ula'-4ulc`

`3ulc=4ula'-ulb`

`color(white)(3ulc)=4((5),(-4))-((6),(8))`

`color(white)(3ulc)=((20),(-16))-((6),(8))=((14),(-24))`

`ulc=1/3((14),(-24))=((14/3),(-8))`

`rArrC=(14/3,-8)`