1. The problem asks to find the result of translating point R(-5,8) by the translation vector T = [-3,-4]. 2. The formula for translation is: $$ (x', y') = (x + t_x, y + t_y) $$ where $(x,y)$ is the original point and $(t_x, t_y)$ is the translation vector. 3. Applying the translation to point R: $$ x' = -5 + (-3) = -5 - 3 = -8 $$ $$ y' = 8 + (-4) = 8 - 4 = 4 $$ 4. Therefore, the translated point is: $$ R' = (-8, 4) $$ This means point R moves 3 units left and 4 units down.