Question

Points A and B are at `(4 ,3 )` and `(1 ,4 )`, respectively. Point A is rotated counterclockwise about the origin by `pi/2` and dilated about point C by a factor of `2`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-7,4)`

Explanation:

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

`• " a point " (x,y)to(-y,x)`

`rArrA(4,3)toA'(-3,4)" where A' is the image of A"`

`"under a dilatation about C of factor 2"`

`vec(CB)=2vec(CA')`

`rArrulb-ulc=2(ula'-ulc)`

`rArrulb-ulc=2ula'-2ulc`

`rArrulc=2ula'-ulb`

`color(white)(rArrulc)=2((-3),(4))-((1),(4))`

`color(white)(rArrulc)=((-6),(8))-((1),(4))=((-7),(4))`

`rArrC=(-7,4)`