To determine the new coordinates of point [tex]\( A'(x', y') \)[/tex] after translating point [tex]\( A(x, y) \)[/tex] by 7 units to the left and 2 units up, we need to apply transformations to the coordinates of point [tex]\( A \)[/tex].
### Step-by-Step Solution:
1. Translation to the Left:
- Moving a point 7 units to the left means we subtract 7 from the x-coordinate.
- Thus, [tex]\( x' = x - 7 \)[/tex].
2. Translation Upwards:
- Moving a point 2 units up means we add 2 to the y-coordinate.
- Thus, [tex]\( y' = y + 2 \)[/tex].
Combining these transformations, the new coordinates [tex]\( (x', y') \)[/tex] of point [tex]\( A' \)[/tex] are given by:
[tex]\[ x' = x - 7 \][/tex]
[tex]\[ y' = y + 2 \][/tex]
Hence, the new point [tex]\( A'(x', y') \)[/tex] after translation is:
[tex]\[ A'(x-7, y+2) \][/tex]
### Final Answer:
The correct option for the new coordinates after translating point [tex]\( A(x, y) \)[/tex] is:
[tex]\[ \boxed{(x-7, y+2)} \][/tex]
