Points A and B are at (5 ,8 )(5,8) and (7 ,2 )(7,2), respectively. Point A is rotated counterclockwise about the origin by pi/2 π2 and dilated about point C by a factor of 4 4. If point A is now at point B, what are the coordinates of point C?
1 Answer
Jun 25, 2018
Explanation:
"under a counterclockwise rotation about the origin of "pi/2under a counterclockwise rotation about the origin of π2
• " a point "(x,y)to(-y,x)∙ a point (x,y)→(−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)
