Points A and B are at (6 ,1 )(6,1) and (3 ,5 )(3,5), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2 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 23, 2018

C=(1/2,-35/4)C=(12,−354)

Explanation:

"under a counterclockwise rotation about the origin of "(3pi)/2under a counterclockwise rotation about the origin of 3π2

• " a point "(x,y)to(y,-x)∙ a point (x,y)→(y,−x)

A(6,1)toA'(1,-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((1),(-6))-((3),(5))

color(white)(4ulc)=((5),(-30))-((3),(5))=((2),(-35))

ulc=1/4((2),(-35))=((1/2),(-35/4))

rArrC=(1/2,-35/4)

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