To find the image of the point \( L(-7, 0) \) under a dilation with center at \( (0, 0) \) and a scale factor of \( 4 \), you can use the following formula for dilation:
\[ L' = (kx, ky) \]
where \( (x, y) \) is the original point and \( k \) is the scale factor.
For the point \( L(-7, 0) \):
- \( x = -7 \)
- \( y = 0 \)
- \( k = 4 \)
Now, applying the dilation:
\[ L' = (4 \cdot -7, 4 \cdot 0) = (-28, 0) \]
Thus, the image of the point \( L \) under the dilation is:
\[ \boxed{(-28, 0)} \]
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