Final answer:
To find the equation of line L, we need to find its slope and its y-intercept. The slope of line L is equal to the negative reciprocal of the slope of the line passing through points A and A'. The y-intercept can be calculated using the coordinate of A and the slope.
Step-by-step explanation:
The reflection of a point across a line can be found by using the midpoint formula and the distance formula. The midpoint formula gives the coordinates of the line's midpoint, and the distance formula gives the distance between the point and the midpoint. To find the equation of line L, we need to find its slope and its y-intercept. The slope of line L is equal to the negative reciprocal of the slope of the line passing through points A and A'. The y-intercept can be calculated using the coordinate of A and the slope. Once we have the slope and y-intercept, we can use the slope-intercept form of a line, y = mx + b, to write the equation for line L.