To determine how the triangle is moved using the translation rule [tex]\((x, y) \rightarrow (x-4, y+1)\)[/tex], we can analyze the transformations applied to the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates.
1. Understanding the translation rule:
- The rule [tex]\((x, y) \rightarrow (x-4, y+1)\)[/tex] indicates that each point [tex]\((x, y)\)[/tex] on the triangle is translated to a new point [tex]\((x-4, y+1)\)[/tex].
2. Translation in the [tex]\(x\)[/tex]-direction:
- The transformation [tex]\(x-4\)[/tex] means that the [tex]\(x\)[/tex]-coordinate of each point is decreased by 4 units.
- Moving in the negative [tex]\(x\)[/tex]-direction is equivalent to moving 4 units to the left.
3. Translation in the [tex]\(y\)[/tex]-direction:
- The transformation [tex]\(y+1\)[/tex] means that the [tex]\(y\)[/tex]-coordinate of each point is increased by 1 unit.
- Moving in the positive [tex]\(y\)[/tex]-direction is equivalent to moving 1 unit up.
Given these transformations:
- The triangle is moved 4 units to the left.
- The triangle is also moved 1 unit up.
Therefore, the correct description of the figure's movement is: four units left and one unit up.
