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GATE 2023 PI – Question 21

Manufacturing Processes II · Computer Integrated Manufacturing · 1 mark · Multiple choice

Find the homogeneous transformation matrix translating point P from (10,15) to (15,25), using column vectors.

  1. $\begin{pmatrix}1&0&5\\0&1&10\\0&0&1\end{pmatrix}$
  2. $\begin{pmatrix}1&0&10\\0&1&5\\0&0&1\end{pmatrix}$
  3. $\begin{pmatrix}5&0&0\\0&10&0\\0&0&1\end{pmatrix}$
  4. $\begin{pmatrix}10&0&0\\0&5&0\\0&0&1\end{pmatrix}$

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Correct answer: (A) $\begin{pmatrix}1&0&5\\0&1&10\\0&0&1\end{pmatrix}$

Explanation

Translation is Δx = 15−10 = 5 and Δy = 25−15 = 10. Place these in the final column of the identity homogeneous matrix. Multiplication by (10,15,1)ᵀ gives (15,25,1)ᵀ. **A**.

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