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'.
<u><em>Slope</em></u>
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
<u><em>Midpoint</em></u>
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)
<em><u>Perpendicular bisector</u></em>
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
