Question

Points A and B are at `(8 ,2 )` and `(5 ,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=(-11/2,8)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

`A(8,2)toA'(-2,8)" 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((-2),(8))-((5),(7))`

`color(white)(rArr2ulc)=((-6),(24))-((5),(7))=((-11),(16))`

`rArrulc=1/2((-11),(16))=((-11/2,8))`

`rArrC=(-11/2,8)`