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 `2`. If point A is now at point B, what are the coordinates of point C?

Answer 1

`C=(-25,-14)`

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)(2)vec(CA')`

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

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

`ulc=2ula'-ulb`

`color(white)(ulc)=2((-9),(-3))-((7),(8))`

`color(white)(ulc)=((-18),(-6))-((7),(8))=((-25),(-14))`

`rArrC=(-25,-14)`