Question

Points A and B are at `(4 ,9 )` and `(7 ,5 )`, respectively. Point A is rotated counterclockwise about the origin by `(3pi)/2` and dilated about point C by a factor of `1/2`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(5,14)`

Explanation:

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

`• " a point "(x,y)to(y,-x)`

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

`rArrvec(CB)=color(red)(1/2)vec(CA')`

`rArrulb-ulc=1/2(ula'-ulc)=1/2ula'-1/2ulc`

`rArr-1/2ulc=1/2a'-ulb`

`color(white)(xxxxxx)=1/2((9),(-4))-((7),(5))=((-5/2),(-7))`

`rArrulc=-2((-5/2),(-7))=((5),(14))`

`rArrC=(5,14)`