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GATE 2016 ME (ME1) – Question 63

Computer Aided Manufacturing and Automation · CAD/CAM and their integration · 2 marks · Multiple choice

The figure below represents a triangle PQR with initial coordinates of the vertices as P(1,3), Q(4,5) and R(5,3.5). The triangle is rotated in the X-Y plane about the vertex P by angle θ in clockwise direction. If sinθ = 0.6 and cosθ = 0.8, the new coordinates of the vertex Q are

Diagram for GATE 2016 ME (ME1) question 63
  1. (4.6, 2.8)
  2. (3.2, 4.6)
  3. (7.9, 5.5)
  4. (5.5, 7.9)

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Show answer and explanation

Correct answer: (A) (4.6, 2.8)

Explanation

Translate Q relative to P: (4−1,5−3)=(3,2). Clockwise rotation gives x-relative=3·0.8+2·0.6=3.6 and y-relative=−3·0.6+2·0.8=−0.2. Add P back to obtain **(4.6,2.8), A**. Rotating about the origin would omit this translation.