Question

Points A and B are at `(9 ,7 )` and `(2 ,5 )`, respectively. Point A is rotated counterclockwise about the origin by `(3pi)/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=(-23/2,11)`

Explanation:

`"under a counterclockwise rotation about the origin of "(3pi)/2`

`• " a point " (x,y)to(-y,x)`

`rArrA(9,7)toA'(-7,9)"where " A' " is the image of A"`

`"under a dilatation about C of factor 3"`

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

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

.`rArr2ulc=3ula'-ulb`

`color(white)(rArr2)=3((-7),(9))-((2),(5))=((-21),(27))-((2),(5))`

`rArrulc=1/2((-23),(22))`

`color(white)(xxxx)=((-23/2),(11))`

`"the components of "ulc" are the coordinates of C"`

`rArrC=(-23/2,11)`