Question

Points A and B are at `(1 ,8 )` and `(3 ,2 )`, 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=(13,-4)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

`rArrA(1,8)toA'(8,-1)" where "A'" is the image of A"`

`"under a dilatation about C of factor 2"`

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

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

`rArrulb-ulc=2ula'-2ulc`

`rArrulc=2ula'-ulb`

`color(white)(rArrulc)=2((8),(-1))-((3),(2))`

`color(white)(rArrulc)=((16),(-2))-((3),(2))=((13),(-4))`

`rArrC=(13,-4)`