Question

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

Explanation:

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

`• " a point "(x,y)to(y,x)`

`rArrA(1,5)toA'(5,1)" 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((5),(1))-((2),(3))`

`color(white)(rArr3ulc)=((20),(4))-((2),(3))=((18),(1))`

`rArrulc=1/3((18),(1))=((6),(1/3))`

`rArrC=(6,1/3)`