Question

Points A and B are at `(4 ,3 )` and `(5 ,1 )`, 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=(7/3,-17/3)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(4,3)toA'(3,-4)" where A' is the image of A"`

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

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

`rArrulb-ulc=4ula'-4ulc`

`rArr3ulc=4ula'-ulb`

`color(white)(rArr3ulc)=4((3),(-4))-((5),(1))`

`color(white)(rArr3ulc)=((12),(-16))-((5),(1))=((7),(-17))`

`rArrulc=1/3((7),(-17))=((7/3),(-17/3))`

`rArrC=(7/3,-17/3)`