To determine the translated coordinates of a point \((x, y)\) when using the translation rule \( T_{-8, 4} \), we need to understand what \( T_{-8, 4} \) means.
The rule \( T_{-8, 4} \) indicates a translation where we subtract 8 from the x-coordinate and add 4 to the y-coordinate.
Here's a step-by-step guide to interpreting this:
1. Translation in the x-direction:
- The translation rule requires us to move every point 8 units to the left. Mathematically, this means we subtract 8 from the x-coordinate.
- If the original x-coordinate is \(x\), the new x-coordinate becomes \(x - 8\).
2. Translation in the y-direction:
- The translation rule requires us to move every point 4 units up. Mathematically, this means we add 4 to the y-coordinate.
- If the original y-coordinate is \(y\), the new y-coordinate becomes \(y + 4\).
Combining these two changes:
- The original point \((x, y)\) gets translated to \((x - 8, y + 4)\).
Thus, another way to express the translation rule \( T_{-8, 4} \) is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 4) \][/tex]
From the given options, this matches:
[tex]\[ (x, y) \rightarrow (x - 8, y + 4) \][/tex]
So, the correct answer is:
[tex]\[ (x, y) \rightarrow (x - 8, y + 4) \][/tex]
Or as given in the choices:
[tex]\[ (x, y) \rightarrow (x - 8, y + 4) \][/tex]
