Question

Points A and B are at `(9 ,3 )` and `(7 ,8 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` 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=(-17,-17/2)`

Explanation:

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

`• " a point "(x,y)to(-x,-y)`

`A(9,3)toA'(-9,-3)" 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((-9),(-3))-((7),(8))`

`color(white)(2ulc)=((-27),(-9))-((7),(8))=((-34),(-17))`

`ulc=1/2((-34),(-17))=((-17),(-17/2))`

`rArrC=(-17,-17/2)`