Question

Points A and B are at `(3 ,7 )` and `(6 ,1 )`, 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(-27/2,4)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

`rArra(3,7)toA'(-7,3)" where A' is the image of A"`

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

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

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

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

`rArr2ulc=3ula'-ulb`

`color(white)(2ulcxxx)=3((-7),(3))-((6),(1))`

`color(white)(xxxxx)=((-21),(9))-((6),(1))=((-27),(8))`

`rArrulc=1/2((-27),(8))=((-27/2),(4))`

`rArrC=(-27/2,4)`