To determine the new coordinates of point \( S' \) after a translation of 6 units up and 4 units to the left, we start with the original coordinates of point \( S \):
\[ S = (2, 2) \]
Step 1: Translate 4 units to the left.
When translating to the left, we subtract from the x-coordinate:
\[ x' = 2 - 4 = -2 \]
Step 2: Translate 6 units up.
When translating up, we add to the y-coordinate:
\[ y' = 2 + 6 = 8 \]
Final Coordinates
Combining these transformations, the new coordinates for point \( S' \) will be:
\[ S' = (-2, 8) \]
Thus, the coordinates of point \( S' \) after the translation are \((-2, 8)\).
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