Points A and B are at (3 ,8 )(3,8) and (7 ,3 )(7,3), 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
Jim G.
Jul 31, 2018

C=(-11/2,-43/4)C=(−112,−434)

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(3,8)toA'(-3,-8)" 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),(-8))-((7),(3))

color(white)(4ulc)=((-15),(-40))-((7),(3))=((-22),(-43))

ulc=1/4((-22),(-43))=((-11/2),(-43/4))

rArrC=(-11/2,-43/4)

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