Question

Points A and B are at `(6 ,5 )` and `(7 ,8 )`, 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=(-17,4)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

`rArrA(6,5)toA'(-5,6)" 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((-5),(6))-((7),(8))`

`color(white)(rArrulc)=((-10),(12))-((7),(8))=((-17),(4))`

`rArrC=(-17,4)`