IGNOU MMTE 4 2026 - Design a program that performs continuous rotation of a hexagon about

Question

Design a program that performs continuous rotation of a hexagon about an arbitrary point (x₀, y₀).
b) Show that reflection about the line y = mx can be achieved by a sequence of rotation, reflection, and inverse rotation operations.

06 Mar 2026

Answer :

Word Count : 382

To perform continuous rotation of a hexagon about an arbitrary point ((x_0, y_0)), the following steps and algorithm can be used: 1. Translate the hexagon so that the rotation point coincides with the origin: For each vertex ((x, y)) of the hexagon, apply translation: [ x' = x - x_0, \quad y' = y - y_0 ] 2. Apply rotation about the origin: For a rotation angle (\theta), the rotated coordinates are: [ x_r = x'\cos\theta - y'\sin\theta, \quad y_r = x'\sin\theta + y'\cos\theta ] 3. Translate the rotated hexagon back to the original reference point: [ x_{\text{final}} = x_r + x_0, \quad y_{\text{final}} = y_r + y_0 ] 4. Repeat continuously: Increment (\theta) in small steps and update the vertex positions

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