14. If a figure is translated with the rule \( T_{\langle-5,3\rangle} \), which translation moves the image back to the original position? (A) \( T_{\langle 5,-3\rangle} \) (B) \( T_{\langle-5,3\rangle} \) (C) \( T_{\langle 0,5\rangle} \) (D) \( T_{\langle-5,0\rangle} \)

To move the figure back to its original position after a translation of \( T_{\langle-5,3\rangle} \), you would need to apply the opposite translation, which reverses the original change. Therefore, the correct translation that does this is \( T_{\langle 5,-3\rangle} \). This translation moves the figure 5 units to the right and 3 units down, effectively canceling out the previous movement. When dealing with translations, it’s important to consider the vectors involved. Many students mistakenly think that applying the same translation again will return the figure to its original position, but instead, remember that you need the exact opposite vector to achieve that perfect reset.