Question

Points A and B are at `(7 ,3 )` and `(5 ,9 )`, respectively. Point A is rotated counterclockwise about the origin by `(3pi)/2` and dilated about point C by a factor of `2`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(1,-23)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`A(7,3)toA'(3,-7)`

`vec(CB)=color(red)(2)vec(CA')`

`ulb-ulc=2(ula'-ulc)`

`ulb-ulc=2ula'-2ulc`

`ulc=2ula'-ulb`

`color(white)(ulc)=2((3),(-7))-((5),(9))`

`color(white)(ulc)=((6),(-14))-((5),(9))=((1),(-23))`

`rArrC=(1,-23)`