If \( \triangle A B C \) is at \( \cdot A(3,6), B(1,7), C(-2,-4) \), and if it is translated right 6 and down 3 , find the coordinate of a \( -B^{\prime} \). Select one: a. \( (-1,3) \) b. \( (5,2) \) c. \( (2,3) \) d. \( (7,4) \)

To find \( B' \), the new coordinates of point \( B \) after the translation, we start with the original coordinates of point \( B(1, 7) \). The translation involves moving it 6 units to the right and 3 units down. 1. Translating right 6: \( 1 + 6 = 7 \) 2. Translating down 3: \( 7 - 3 = 4 \) Thus, the new coordinates of point \( B' \) are \( (7, 4) \). Now, we are looking for \( -B' \), which means we take the negative of both coordinates of \( B' \): - The x-coordinate: \( -7 \) - The y-coordinate: \( -4 \) So, \( -B' \) has coordinates \( (-7, -4) \), but it seems the options given do not include this result. Therefore, if your question actually meant to find \( B' \)'s coordinates, then the correct answer is \( (7, 4) \), which corresponds to option d.