Question

Points A and B are at `(7 ,1 )` and `(3 ,7 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` and dilated about point C by a factor of `3`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-12,-5)`

Explanation:

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

`• " a point "(x,y)to(-x,-y)`

`rArrA(7,1)toA'(-7,-1)" where A' is the image of A"`

`rArrvec(CB)=color(red)(3)vec(CA')`

`rArrulb-ulc=3(ula'-ulc)`

`rArrulb-ulc=3ula'-3ulc`

`rArr2ulc=3ula'-ulb`

`color(white)(rArr2ulc)=3((-7),(-1))-((3),(7))`

`color(white)(rArr2ulc)=((-21),(-3))-((3),(7))=((-24),(-10))`

`rArrulc=1/2((-24),(-10))=((-12),(-5))`

`rArrC=(-12,-5)`