Bisect two arcs above and below the given points or line and the perpendicular of these arcs cuts through the midpoint.
Draw a line joining a point and its image and find its midpoint. Repeat for another pair of point and its image. The line joining these midpoints is the line of reflection.
This can be done with the equation (x1+x2)/2, (y1+y2)/2 which, when solved, creates a (x,x) solution, or a coordinate pair solution. if you had the points (2,4) and (4,8) you would put x1 (2) plus (+) x2 (4) divided by 2, and 2+4 is 6, and 6/2 is 3, so we know our midpoint x value is 3. Then, we would plug in our 'y' values, so we would have y1 (4) + y2 (8) and 4+8 = 12 and 12/2 is 6, so our solution coordinate ordered pair would be (3,6).
The horizontal distance between them is from -5 to 1, that is 6 units. The vertical distance between them is from 1 to 6, that is 5 units. So, using Pythagoras, the distance between then, along the diagonal, is sqrt(62 + 52) = sqrt(36 + 25) = sqrt(61) units.
Infinitely many. There are infinitely many points in the plane and although any pair of points define a line, no matter how many lines you are given, it is always possible to find a point that is not on any of them - that is, a point that is not collinear.