3 points
The answer is infinite number of lines
There are an infinity of points 4cm from a given line. These points form 2 lines parallel to and either side of the original line. Equally, there are an infinite number of points 4cm from a given point on the original line. These points lie on the circumference of a circle radius 4cm with its centre at the given point. There are only 2 points that fulfil both conditions. These points are found on the circumference of the circle where a diameter perpendicular to the original line and passing through the given point meets the circumference of the circle. These two points are also where the two parallel lines form tangents with the circle.
The slope of a line can be found by choosing any two points of that single line, not of multiple lines.
1
2 lines, I believe.
One.
Just one.
One.
Through any two distinct points, exactly one straight line can be drawn. If you have more than two points, the number of lines that can be drawn depends on how many of those points are distinct and not collinear. For ( n ) distinct points, the maximum number of lines that can be formed is given by the combination formula ( \binom{n}{2} ), which represents the number of ways to choose 2 points from ( n ). If some points are collinear, the number of unique lines will be less.
The points are Dependent. Just pot the points and put two arrows at the end of the lines.
The answer will depend on the relative positions of the points.
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.