Question

Points A and B are at `(3 ,5 )` and `(6 ,1 )`, respectively. Point A is rotated counterclockwise about the origin by `pi/2` 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=(-21/2,4)`

Explanation:

`"under a counterclockwise rotation about the origin of "pi/2`

.`• " a point "(x,y)to(-y,x)`

`rArrA(3,5)toA'(-5,3)" 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((-5),(3))-((6),(1))`

`color(white)(rArr2ulc)=((-15),(9))-((6),(1))=((-21),(8))`

`rArrulc=1/2((-21),(8))=((-21/2),(4))`

`rArrC=(-21/2,4)`