Question

With a two dimensional surface, if we take (2, 1) as the center point and consider

a transformation with a rotation angle of 45◦, then point (3, 3) is transformed

into point (----)?​

Answer 1

Explanation:

Distance between (2,1) and (3,3) = √5

parametric equations for circle of radius √5, centered at (2,1):

x = √5cosθ+2

y = √5sinθ+1

At (3,3), θ = arccos(1/√5) ≅ 63.4°

After 45° transformation:

θ' = 63.4° + 45° = 108.4°

x' = √5cos(108.4°)+2 = 1.29

y' = √sin(108.4°)+1 = 3.12

(3,3) transformed to (1.29,3.12)