Question

Points A and B are at `(2 ,9 )` and `(8 ,6 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` and dilated about point C by a factor of `4`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-16/3,-14)`

Explanation:

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

`• " a point "(x,y)to(-x-y)`

`rArrA(2,9)toA'(-2,-9)" where A' is the image of A"`

`rArrvec(CB)=color(red)(4)vec(CA')`

`rArrulb-ulc=4(ula'-ulc)`

`rArrulb-ulc=4ula'-4ulc`

`rArr3ulc=4ula'-ulb`

`color(white)(rArr3ulc)=4((-2),(-9))-((8),(6))`

`color(white)(rArr3ulc)=((-8),(-36))-((8),(6))=((-16),(-42))`

`rArrulc=1/3((-16),(-42))=((-16/3),(-14))`

`rArrC=(-16/3,-14)`