Question

Points A and B are at `(9 ,4 )` and `(1 ,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=(-13/2,25/2)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

`rArrA(9,4)toA'(-4,9)" 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)(rArrulc)=3((-4),(9))-((1),(2))`

`color(white)(rArrulc)=((-12),(27))-((1),(2))=((-13),(25))`

`rArrulc=1/2((-13),(25))=((-13/2),(25/2))`

`rArrC=(-13/2,25/2)`