Which of the following translations corresponds to the matrix ? a A segment is shifted 2 units up and 3 units to the left.
b A triangle is shifted 2 units to the right and 3 units down.
c A segment is shifted 2 units to the right and 3 units down.
d A triangle is shifted 2 units up and 3 units to the left.
A segment is shifted 2 units up and 3 units to the left.
A triangle is shifted 2 units to the right and 3 units down.
A segment is shifted 2 units to the right and 3 units down.
A triangle is shifted 2 units up and 3 units to the left.
To determine which translation corresponds to the given matrix, you will need to understand how translations are represented using matrix notation.
In matrix notation, a translation can be represented by a 2x2 matrix called a translation matrix. The translation matrix has the following form:
| 1 0 |
| dx dy |
Where dx represents the horizontal translation and dy represents the vertical translation.
Now let's analyze the given matrix:
| 1 0 |
| -3 2 |
The elements in the first row indicate that there is no horizontal translation (dx = 0) and no vertical translation (dy = 0), so option A can be eliminated.
The elements in the second row indicate a vertical translation of 2 units up (dy = -3) and a horizontal translation of 3 units to the left (dx = 2). Therefore, the correct translation is option D: "A triangle is shifted 2 units up and 3 units to the left."