A 36- degree counterclockwise rotation centered at the origin sends the point A=(6,3) to the image point A'.

Question

To three decimal places, find coordinates for A'.

 

 

Please help get me the answer.

Answer 1

First, get the length of the line from (0,0) to (6,3):

 

r = sqrt(6² + 3²) = 6.7082

 

Now get the angle it makes with respect to the x-axis:

 

θ = tan^-1(y/x) = tan^-1(3/6) = 26.5651 degrees

 

Add 36 degrees to θ:

 

θ' = 36+26.5651 = 62.5651 degrees

 

r' = r (pure rotation)

 

x' = r*cos(θ') = 6.7082*cos(62.5651) = 3.0907

 

y' = r*sin(θ') = 6.7082*sin(62.5651) = 5.9538

 

A' is (3.0907, 5.9538)