Question

Points A and B are at `(6 ,1 )` and `(8 ,9 )`, 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=(-13,-6)`

Explanation:

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

`• " a point "(x,y)to(-x,-y)`

`rArrA(6,1)toA'(-6,-1)" where A' is the image of A"`

`"under a dilatation about C of factor 3"`

`vec(CB)=3vec(CA')`

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

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

`rArr2ulc=3ula'-ulb`

`color(white)(rArr2ulc)=3((-6),(-1))-((8),(9))`

`color(white)(rArrulc)=((-18),(-3))-((8),(9))=((-26),(-12))`

`rArrulc=1/2((-26),(-12))=((-13),(-6))`

`rArrC=(-13,-6)`