Question

Points A and B are at `(2 ,7 )` and `(4 ,6 )`, 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=(-5,-27/2)`

Explanation:

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

`• " a point "(x,y)to(-x,-y)`

`rArrA(2,7)toA'(-2,-7)" where A' is the image of A"`

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

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

`rArrulb-ulc=3ula'-3ulc`

`rArr2ulc=3ula'-ulb`

`color(white)(rArr2ulc)=3((-2),(-7))-((4),(6))`

`color(white)(rArr2ulc)=((-6),(-21))-((4),(6))=((-10),(-27))`

`rArrulc=1/2((-10),(-27))=((-5),(-27/2))`

`rArrC=(-5,-27/2)`