Question

Points A and B are at `(5 ,8 )` and `(8 ,1 )`, respectively. Point A is rotated counterclockwise about the origin by `pi` 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=(-40/3,-7)`

Explanation:

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

`• " a point "(x,y)to(-x-y)`

`rArrA(5,8)toA'(-8,-5)" where A' is the image of A"`

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

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

`rArrulb-ulc=4ula'-4ulc`

`rArr3ulc=4ula'-ulb`

`color(white)(rArrul3c)=4((-8),(-5))-((8),(1))`

`color(white)(rArrul3c)=((-32),(-20))-((8),(1))=((-40),(-21))`

`rArrulc=1/3((-40),(-21))=((-40/3),(-7))`

`rArrC=(-40/3,-7)`