Points A and B are at (6 ,5 ) and (3 ,8 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 and dilated about point C by a factor of 2 . If point A is now at point B, what are the coordinates of point C?

2 Answers
sankarankalyanam
Jun 8, 2018

color(green)("Coordinates of " C = (-13,4)

Explanation:

A (6,5), B(3,8), " rotated counter clockwise by " pi/2 " and dilated by factor 2"

Coordinates of A after pi/2 counter clockwise rotation is

A(6,5) -> A'(-5,6)

vec(BC) = 2 vec(A'C)

b - c = 2 (a' - c)

c = 2a' - b

C((x),(y)) = 2 ((-5),(6)) - ((3),(8)) =color(green)( ((-13),(4))

Jim G.
Jun 8, 2018

C=(-13,4)

Explanation:

"under a counterclockwise rotation about the origin of "pi/2

• " a point "(x,y)to(-y,x)

A(6,5)toA'(-5,6)" where A' is the image if A"

vec(CB)=color(red)(2)vec(CA')

ulb-ulc=2(ula'-ulc)

ulb-ulc=2ula'-2ulc

ulc=2ula'-ulb

color(white)(ulc)=2((-5),(6))-((3),(8))

color(white)(ulc)=((-10),(12))-((3),(8))=((-13),(4))

rArrC=(-13,4)

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