To determine how the triangle is moved, we analyze the translation rule given: [tex]\((x, y) \rightarrow (x-4, y+1)\)[/tex].
1. Horizontal Movement:
- The translation rule shows that [tex]\(x\)[/tex] is replaced by [tex]\(x-4\)[/tex].
- Subtracting 4 from [tex]\(x\)[/tex] means that for every point on the triangle, the x-coordinate decreases by 4.
- A decrease in the x-coordinate by 4 units means the figure is moved 4 units to the left.
2. Vertical Movement:
- The translation rule shows that [tex]\(y\)[/tex] is replaced by [tex]\(y+1\)[/tex].
- Adding 1 to [tex]\(y\)[/tex] means that for every point on the triangle, the y-coordinate increases by 1.
- An increase in the y-coordinate by 1 unit means the figure is moved 1 unit up.
Therefore, the triangle is translated 4 units to the left and 1 unit up.
So, the option that correctly describes how the figure is moved is:
four units left and one unit up.
