Question

Points A and B are at `(2 ,9 )` and `(3 ,7 )`, respectively. Point A is rotated counterclockwise about the origin by `pi/2` 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=(-15,-1/2)`

Explanation:

`"under a counterclockwise rotation about the origin of "pi/2`

`• " a point "(x,y)to(-y,x)`

`rArrA(2,9)toA'(-9,2)" 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((-9),(2))-((3),(7))`

`color(white)(rArr2ulc)=((-27),(6))-((3),(7))=((-30),(-1))`

`rArrulc=1/2((-30),(-1))=((-15),(-1/2))`

`rArrC=(-15,-1/2)`