Question

Points A and B are at `(5 ,9 )` and `(8 ,6 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` 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=(-18,-24)`

Explanation:

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

`• " a point "(x,y)to(-x,-y)`

`A(5,9)toA'(-5,-9)" where A' is the image of A"`

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

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

`ulb-ulc=2ula'-2ulc`

`ulc=2ula'-ulb`

`color(white)(ulc)=2((-5),(-9))-((8),(6))`

`color(white)(ulc)=((-10),(-18))-((8),(6))=((-18),(-24))`

`rArrC=(-18,-24)`