To find the coordinates of point \( A' \) after translating point \( A(4, 7) \) left 2 units and down 4 units, you can follow these steps:
-
Translate left 2 units:
- To translate left, you subtract from the x-coordinate.
- \( 4 - 2 = 2 \)
-
Translate down 4 units:
- To translate down, you subtract from the y-coordinate.
- \( 7 - 4 = 3 \)
Therefore, the new coordinates for point \( A' \) after the translation will be:
\[ A' (2, 3) \]