Question

Points A and B are at `(8 ,3 )` and `(5 ,4 )`, 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=(-7,10)`

Explanation:

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

`• " a point "(x,y)to(-y,x)`

`A(8,3)toA'(-3,8)" where A' is the image of A"`

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

`ulb-ulc=3(ula'-ulc)`

`ulb-ulc=3ula'-3ulc`

`2ulc=3ula'-ulb`

`color(white)(2ulc)=3((-3),(8))-((5),(4))`

`color(white)(2ulc)=((-9),(24))-((5),(4))=((-14),(20))`

`ulc=1/2((-14),(20))=((-7),(10))`

`rArrC=(-7,10)`