Final answer:
After reflecting over the x-axis, the new coordinates for Vertex L are (1, -4), as the x-coordinate remains the same and the y-coordinate changes sign.
Step-by-step explanation:
When reflecting a point over the x-axis, the x-coordinate remains the same but the y-coordinate changes its sign. For Vertex L with initial coordinates (1, 4), after reflection over the x-axis, the new y-coordinate will be -4 since it is the opposite of the original y-coordinate. Therefore, the new coordinates for Vertex L after the reflection will be (1, -4).