To find the image of the point \( A(-5, 5) \) under a dilation with center \( (0, 0) \) and a scale factor of \( 1.2 \), you can use the formula:
\[ A' = (kx, ky) \]
where \( k \) is the scale factor and \( (x, y) \) are the coordinates of point \( A \).
In this case:
- \( k = 1.2 \)
- \( A(-5, 5) \), so \( x = -5 \) and \( y = 5 \).
Calculating the new coordinates:
\[ A' = (1.2 \cdot -5, 1.2 \cdot 5) \]
Calculating each coordinate:
- \( 1.2 \cdot -5 = -6 \)
- \( 1.2 \cdot 5 = 6 \)
Thus, the image of the point \( A \) after dilation is:
\[ A' = (-6, 6) \]
So, in ordered pair form, the answer is:
\[ \boxed{(-6, 6)} \]