The pre image LMNO was translated using the rule (x + 5 , y + 7) to create the image L'M'N'O'.
L (-5 , -4) → (-5 + 5 , -4 + 7) → L' (0 , 3)
M (-7 , -1) → (-7 + 5 , -1 + 7) → M' (-2 , 6)
N (-1 , -1) → (-1 + 5 , -1 + 7) → N' (4 , 6)
O (-2 , -4) → (-2 + 5 , -4 + 7) → O' (3 , 3)
Hope this helps :)