Question

Points A and B are at `(9 ,7 )` and `(3 ,4 )`, respectively. Point A is rotated counterclockwise about the origin by `pi/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=(-17,14)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

`rArrA(9,7)toA'(-7,9)" where A' is the image of A"`

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

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

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

`rArrulc=2ula'-ulb`

`color(white)(rArrulc)=2((-7),(9))-((3),(4))`

`color(white)(rArrulc)=((-14),(18))-((3),(4))=((-17),(14))`

`rArrC=(-17,14)`