Points A and B are at (3 ,6 ) and (7 ,3 ), respectively. Point A is rotated counterclockwise about the origin by pi and dilated about point C by a factor of 5 . If point A is now at point B, what are the coordinates of point C?

1 Answer
Jul 20, 2018

C=(-11/2,-33/4)

Explanation:

"under a counterclockwise rotation about the origin of "pi

• " a point "(x,y)to(-x,-y)

A(3,6)toA'(-3,-6)" where A' is the image of A"

vec(CB)=color(red)(5)vec(CA')

ulb-ulc=5(ula'-ulc)

ulb-ulc=5ula'-5ulc

4ulc=5ula'-ulb

color(white)(4ulc)=5((-3),(-6))-((7),(3))

color(white)(4ulc)=((-15),(-30))-((7),(3))=((-22),(-33))

ulc=1/4((-22),(-33))=((-11/2),(-33/4))

rArrC=(-11/2,-33/4)