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Parallel
Parallel lines will never intersect. They will stay an equal distance apart at all points.
Lines can by parallel or not parallel. This property does not apply to points.
Points cannot be parallel to other points. A straight line joining two points is parallel to a straight line joining another pair of points if the gradient (slope) of the two lines is the same.
Points cannot be parallel or perpendicular. So they never are.
Reflection
Suppose the specified line has gradient m. Also suppose the specified distance is d.Then x = sqrt[d2/(1 + m2)] and y = m*x.A translation, by a distance x in the horizontal direction and y=mx in the vertical direction will move the point by the specified distance in the direction of the specified line.
A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).A circle is the set of all points, on a plane, that is at a specific distance from a specified point (the center).
translation
Two or more lines that are the same distance at all points are called parallel lines.
Parallel
the same distance
Yes, in geography, all points along a parallel of latitude are indeed the same distance from the equator. This is because parallels are imaginary lines that run parallel to the equator, maintaining the same distance from it as they wrap around the Earth.
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.
Parallel lines are the same distance apart for all points along the line.
Parallel lines will never intersect. They will stay an equal distance apart at all points.
Lines can by parallel or not parallel. This property does not apply to points.