The original poster attempts to find the equations of two straight lines that are inclined at an angle of 45° to the line represented by the equation 2x + y - 3 = 0, while passing through the point (-1, 4). The problem involves understanding the relationship between the slopes of the lines and the angle between them.
Participants are actively engaging with the problem, questioning the assignment of slopes and discussing the implications of swapping m1 and m2. There is a recognition that both positive and negative angles are relevant to the problem, indicating a productive exploration of the topic.
The discussion includes considerations about the nature of angles formed by slopes and the specific conditions of the problem, such as the requirement for the lines to be at a 45° angle to a given line.
That just says the angle between the m1 and m2 lines is θ. Whether you consider that as plus or minus depends on which of the two lines you start from. In the present problem you are asked for two lines at angle 45 degrees to a given line, so you want both cases.Kurokari said:Well what about if there is a negative and and a positive?
Say m1 = -1 and m2 = 2
If we followed the formula, I would get a tanθ,
However if I were to swap them, I would instead get a negative tanθ. Or does this matter?