Question

Points A and B are at `(3 ,7 )` and `(2 ,4 )`, respectively. Point A is rotated counterclockwise about the origin by `pi/2` and dilated about point C by a factor of `4`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-10,8/3)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

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

`vec(CB)=color(red)(4)vec(CA')`

`ulb-ulc=4(ula'-ulc)`

`ulb-ulc=4ula'-4ulc`

`3ulc=4ula'-ulb`

`color(white)(3ulc)=4((-7),(3))-((2),(4))`

`color(white)(3ulc)=((-28),(12))-((2),(4))=((-30),(8))`

`ulc=1/3((-30),(8))=((-10),(8/3))`

`rArrC=(-10,8/3)`