Points A and B are at (3 ,6 )(3,6) and (7 ,5 )(7,5), respectively. Point A is rotated counterclockwise about the origin by pi π and dilated about point C by a factor of 5 5. If point A is now at point B, what are the coordinates of point C?
1 Answer
Jun 11, 2018
Explanation:
"under a counterclockwise rotation about the origin of "piunder a counterclockwise rotation about the origin of π
• " a point "(x,y)to(-x,-y)∙ a point (x,y)→(−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),(5))
color(white)(4ulc)=((-15),(-30))-((7),(5))=((-22),(-35))
ulc=1/4((-22),(-35))=((-11/2),(-35/4))
rArrC=(-11/2,-35/4)
