Points A and B are at (5 ,8 ) and (7 ,2 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 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?
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1 Answer
Jun 25, 2018
Explanation:
"under a counterclockwise rotation about the origin of "pi/2
• " a point "(x,y)to(-y,x)
A(5,8)toA'(-8,5)" where A' is the image of A"
vec(CB)=color(red)(4)vec(CA')
ulb-ulc=4(ula'-ulc)
ulb-ulc=4ula'-4ulc
3ulc=4ula'-ulb
color(white)(3ulc)=4((-8),(5))-((7),(2))
color(white)(3ulc)=((-32),(20))-((7),(2))=((-39),(18))
ulc=1/3((-39),(18))=((-13),(6))
rArrC=(-13,6)
