Question

Points A and B are at `(6 ,3 )` and `(1 ,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=(-19/2,-9)`

Explanation:

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

`"a point "(x,y)to(-x,-y)`

`rArrA(6,3)toA'(-6,-3)" 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((-6),(-3))-((1),(9))`

`color(white)(rArr2ulc)=((-18),(-9))-((1),(9))=((-19),(-18))`

`rArrulc=1/2((-19),(-18))=((-19/2),(-9))`

`rArrC=(-19/2,-9)`