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If the gradients (slopes) of the lines are the same or if both lines are vertical, then the lines are parallel.If the product of the two slopes of -1 then the lines are perpendicular. Also, if one of the lines is horizontal (slope = 0) and the other is vertical (slope undefined), then they are perpendicular. In all other cases, the lines are neither parallel nor perpendicular.

Q: How is it determined whether the lines passing through some specified points are parallel perpendicular or neither?

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No, neither.

If the slope of the equations are the same then they are parallel If the slope of the equations are minus reciprocal then they are perpendicular If the slope of the equations are different then they are neither

neither, a regular hexagon's sides hit at a 120 degree angle so they are neither parallel nor perpendicular. An irregular hexagon's can, but usually don't. In a regular hexagon (all 6 sides congruent), opposite sides are parallel.

Points cannot be parallel or perpendicular. So they never are.

Neither perpendicular nor parallel

Related questions

Parallel

No, neither.

Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if the product of their slopes is -1. If neither of these conditions are met, the lines are nether parallel, or perpendicular.

Diagonal

No, oblique lines are neither parallel nor perpendicular

A rhombus has opposite equal parallel sides

If the slope of the equations are the same then they are parallel If the slope of the equations are minus reciprocal then they are perpendicular If the slope of the equations are different then they are neither

Neither: because one line, by itself, can be neither parallel or perpendicular. These characteristics are relevant only in the context of another line (or lines). The given line is parallel to some lines and perpendicular to others.

If they have the same slope, they are parallel. The slopes are the same, so yes they are parallel.

neither

parallel is easy. are they the same distance apart at two different benchmarks? if not then they may be perpendicular. perpendicular means they intersect at a 90 degrees. If it is any other angle and they are different distances apart at your two benchmarks then they are neither of the two choices

In two dimensions: They are parallel if their gradients are the same. They are perpendicular if the product of their gradients is -1. Otherwise they are neither. The nature of the question suggests that you have not yet studied lines in 3 or more dimensions.