The user is providing the following image:
which shows a rectangle of vertices ABCD that is reflected over the x-axis.
We notice that the vertices of the original image are located at:
A = (-4, -2)
B = (4, -2)
C = (4, -4)
D = (-4, -4)
Then, if we need to replect these values around the x axis, we will have to :
1) keep all the x-coordinates of the points intact, and flip to their opposite values the y-coordinates of such vertices. That means that the image after the reflection has the following vertices:
A' = (-4, 2)
B' = (4, 2)
C' = (4, 4)
D' = (-4, 4)
The length of the side AD equals the length of side BC = 2 units which is also equal to the lengths of the new sides : A'D' , and B'C'. This can be obtained via counting the number of divisions on the plot, or using the difference between y-coordinates for points A and D (-2 - (-4) = 4-2 = 2), or B and C (-2 - (-4) = 4 - 2 = 2)
And the length of the side AB equals the length of side CD = 8 units . his can be obtained via counting the number of divisions that separate the vertices on the plot, or using the difference between x-coordinates for points A and B (4 - (-4) = 8), or C and D. Notice as well that the reflection we performed keeps the dimension without change, so 8 units is also the length of sides A'B' and C'D' of the image.