Question

Points A and B are at `(5 ,7 )` and `(8 ,6 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` 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=(-18,-20)`

Explanation:

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

`• " a point "(x,y)to(-x,-y)`

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

`color(white)(rArrulc)=((-10),(-14))-((8),(6))=((-18),(-20))`

`rArrC=(-18,-20)`