Answer:
x = 0
Step-by-step explanation:
D = (-8, -3), D' = (8, -3)
The line of reflection is the perpendicular bisector of the segment between these points. In order to find that, we need to know the slope and midpoint of the segment DD'.
Slope
The slope of the line DD' is ...
... m = (change in y)/(change in x) = (-3 -(-3))/(8 -(-8)) = 0/16 = 0
The line through point D with slope 0 is ...
... y = 0(x -(-8)) +(-3)
... y = -3
Midpoint
The midpoint of the segment DD' is the average of their coordinates:
... M = (D +D')/2 = ((-8, -3) +(8, -3))/2 = (-8+8, -3-3)/2 = (0, -3)
Perpendicular bisector
The line perpendicular to the horizontal line y=-3 through the point M = (0, -3) will be a vertical line of the form ...
... x = constant
The x-coordinate of the point (0, -3) tells us the constant, so the line of reflection is ...
... x = 0
