Question

Transformation matrix to translate a point P from (10, 15) to (15, 25) is

• A. \[ \begin{bmatrix} 1 & 0 & 5 \\ 0 & 1 & 10 \\ 0 & 0 & 1 \end{bmatrix} \]
• B. \[ \begin{bmatrix} 1 & 0 & 10 \\ 0 & 1 & 5 \\ 0 & 0 & 1 \end{bmatrix} \]
• C. \[ \begin{bmatrix} 5 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]
• D. \[ \begin{bmatrix} 10 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]

Hint:

To translate a point in a 2D plane, the transformation matrix includes the change in coordinates along the x and y axes as translation terms.

Answer 1

The Correct Option is A

- To find the translation matrix, we need to move the point from $(10, 15)$ to $(15, 25)$. The change in coordinates is $(\Delta x, \Delta y) = (15-10, 25-15) = (5, 10)$.
- The translation matrix to shift a point by $(\Delta x, \Delta y)$ is \[ \begin{bmatrix} 1 & 0 & \Delta x \\ 0 & 1 & \Delta y \\ 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 5 \\ 0 & 1 & 10 \\ 0 & 0 & 1 \end{bmatrix}. \] Thus, the correct answer is (A).