To determine how the triangle is translated, we need to apply the given translation rule to the coordinates [tex]\((x, y)\)[/tex]. The rule provided is [tex]\((x, y) \rightarrow (x-4, y+1)\)[/tex].
Let's break down this rule:
- For the [tex]\(x\)[/tex]-coordinate: [tex]\(x-4\)[/tex]
- This means we are subtracting 4 from the original [tex]\(x\)[/tex]-coordinate, which translates the point 4 units to the left.
- For the [tex]\(y\)[/tex]-coordinate: [tex]\(y+1\)[/tex]
- This means we are adding 1 to the original [tex]\(y\)[/tex]-coordinate, which translates the point 1 unit up.
Therefore, the translation rule indicates that the triangle is moved four units to the left and one unit up.
Thus, the correct description of the movement is:
- "four units left and one unit up."
