Question

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

Answer 1

`C=(9/2,-7)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(3,5)toA'(5,-3)" where A' is the image of A"`

`rArrvec(CB)=color(red)(3)vec(CA')`

`rArrulb-ulc=3(ula'-ulc)`

`rArrulb-ulc=3ula'-3ulc`

`rArr2ulc=3ula'-ulb`

`color(white)(rArr2ulc)=3((5),(-3))-((6),(5))`

`color(white)(rArr2ulc)=((15),(-9))-((6),(5))=((9),(-14))`

`rArrulc=1/2((9),(-14))=((9/2),(-7))`

`rArrC=(9/2,-7)`