Question

Points A and B are at `(2 ,6 )` and `(6 ,9 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` 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=(14,24)`

Explanation:

`"under a counterclockwise rotation about the origin of "pi`

`• " a point "(x,y)to(-x,-y)`

`A(2,6)toA'(-2,-6)" where A' is the image of A"`

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

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

`ulb-ulc=1/2ula'-1/2ulc`

`1/2ulc=ulb-1/2ula'`

`color(white)(1/2ulc)=((6),(9))-1/2((-2),(-6))`

`color(white)(1/2ulc)=((6),(9))-((-1),(-3))=((7),(12))`

`ulc=2((7),(12))=((14),(24))`

`rArrC=(14,24)`