To determine the line of reflection that produces Y′(9, 3), we need to find the midpoint between Y and Y′, which we can call M. We can then find the slope of the line that passes through Y and M, and then find the perpendicular line that passes through M. This perpendicular line is the line of reflection.
First, let's find the coordinates of M:
M = ((-9 + 9)/2, (3 + 3)/2)
M = (-9/2, 3)
The slope of the line passing through Y and M is:
m = (3 - 3)/(-9 - (-9/2))
m = 0
Since the slope is 0, the line passing through Y and M is a horizontal line. The equation of this line is:
y - 3 = 0
Now we need to find the perpendicular line that passes through M. Since the slope of the line passing through Y and M is 0, the slope of the perpendicular line is undefined. This perpendicular line is a vertical line passing through M. The equation of this line is:
x - (-9/2) = 0
Simplifying this equation, we get:
x + 9/2 = 0
Therefore, the line of reflection that produces Y′(9, 3) is the vertical line x + 9/2 = 0.