Aug2016 cs Q16

0. A point P(2, 5) is rotated about a pivot point (1, 2) by 60°. What is the new transformed point P' ?

Answer
Comment
Array

Option : B
Explanation :
Transformation of an object point Q(x, y), θ° about a fixed center of rotation P(h, k)
step 1: Translate so that the center of rotation P is at the origin
step 2: Perform a rotation of θ° about the origin, and
step 3: Translate P back to (h, k)
using V = hi + kj as translation vector
R_θ,P = T_-v R_θ T_v

θ = 60°, h = 1, k = 2, Q(x, y) = (2, 5)
Q' = Q.R_60,P

so,
x' = (3-5.196)/2 = -2.196/2 = -1.098 ≅ -1
y' = (7+1.732)/2 = 8.1732/2 = 4.0866 ≅ 4
So, option (B) i.e (-1, 4) is the answer

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