Question

Points A and B are at `(9 ,4 )` and `(7 ,2 )`, 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=(5/2,-29/2)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`A(9,4)toA'(4,-9)" where A' is the image of A"`

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

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

`ulb-ulc=3ula'-3ulc`

`2ulc=3ula'-ulb`

`color(white)(2ulc)=3((4),(-9))-((7),(2))`

`color(white)(2ulc)=((12),(-27))-((7),(2))=((5),(-29))`

`ulc=1/2((5),(-29))=((5/2),(-29/2))`

`rArrC=(5/2,-29/2)`