The vertices of figure KLMN are K(1, 1), L(4, 1), M(2, 3), and N(5, 3). If KLMN is reflected across the line y=-1, find the coordinates of vertex L'.​

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':

2. y-coordinate of L'

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

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:

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