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The coordinates of the vertex L' are (4, -3).

Explanation:

A reflection accross the line y = - 1 will produce images with the same x-coordinate and change the - coordinate.

The y-coordinate of the image will be at the same distance from the line y = - 1 as the pre-image, on the other side of the line.

The vertex L has coordinates (4,1).

1. x-coordinate of L':

same x-coordinate of (4,1): 4.

2. y-coordinate of L'

i) Determine the distance distance between L(4,1) and y = - 1:

|  1 - (-1)| = 2

ii) Shift the y-coordinate of the line two units downward (because L is above the line, L' will be below the line).  Then subtract 2 from - 1:

- 1 - 2 = - 3

Thus, the y-coordinate of L' will be - 3.

Hence, the resultant coordinates of vertex L' are (4, -3)