Question

Points A and B are at `(8 ,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 `3`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(13/2,-27/2)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(8,5)toA'(5,-8)" where A' is the image of A"`

`"under a dilatation about C of factor 3"`

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

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

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

`rArr2ulc=3ula'-ulb`

`color(white)(xxxx)=3((5),(-8))-((2),(3))`

`color(white)(xxxx)=((15),(-24))-((2),(3))=((13),(-27))`

`rArrulc=1/2((13),(-27))=((13/2),(-27/2))`

`rArrC=(13/2,-27/2)`